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In the Single-Input-Single-Output (SISO) setting, Negative Imaginary (NI) systems refer to systems with negative frequency response for all positive frequencies. The NI theory was motivated by the study of inertial systems with collocated position sensor and force actuator. This type of systems can have nonminimum phase zero, be improper and have up to a relative degree of two. Thus, stability analysis and controller synthesis using passivity theorem may not be applicable. Moreover, using traditional design techniques such as H∞ and H₂ to control this kind of systems may lead to conservative results and poor performance due to the oscillatory nature of the systems and the effect of the unmodelled dynamics on the closed-loop system performance. The NI property can be observed in a number of physical systems such as cantilever beams, large space structures, robotic manipulators, gantry crane systems, vibration shock absorbers, series elastic actuators and mechatronic systems. This, in addition to the simple internal stability result of interconnected NI systems, which depends only on the DC loop gain, has made the theory appealing for practical engineering applications. Example of some of these applications include vibration control of lightly-damped flexible structure, motion control of robotic arm, the control of a DC servo motor, nano-positioning control of an atomic force microscope, consensus control of multi-agent systems, to mention but a few. Due to the vast areas of application of the NI theory, controller synthesis techniques that achieve some transient performance level, such as prescribed decay rate, becomes imperative. This thesis therefore focuses on the synthesis technique of such controllers. A set of Linear Matrix Inequalities (LMIs) conditions are proposed for the synthesis of a dynamic output feedback controller. These LMIs render the closed-loop system to be NI and ensure that the DC gain condition for closed-loop internal stability is satisfied. The proposed conditions also ensures that the closed-loop system has prescribed decay rate via the α-pole placement technique. The thesis then introduces a new class of NI systems called the Linear Time-Varying (LTV) NI systems. First, a time domain definition is provided, before a state-space characterization is proposed using Linear Differential Matrix Inequalities (LDMIs). Furthermore, a specialized case of the LTV NI systems called the Linear Parameter-Varying (LPV) NI systems are introduced. The state-space characterization of the LPV NI systems is provided using LMIs. Finally, a set of sufficient conditions for the stability of two asymptotically stable LTV NI systems is proposed and the result is shown to specialise to the LPV NI systems case. Also, this thesis introduces a robust controller synthesis technique using the principles of Internal Model Control (IMC) and NI theory. In the proposed technique, the design of the Youla parameter is cast as an NI controller synthesis problem. Two different synthesis methods are provided, both of which are sufficient conditions. One is an LMI-based approach and the other is a frequency domain approach. Finally, the thesis deals with hardware validation of the proposed LMI-based IMC NI controller synthesis technique. The efficacy of the technique is demonstrated on a flexible cantilever beam with collocated position sensor and force actuator. The controller is designed to attenuate the vibration of the flexible structure caused by external disturbances.

This thesis investigates multi-agent systems problems for systems with negative imaginary dynamics. Via tools from negative imaginary theory and graph theory, this research addresses the following three multi-agent systems problems: (i) the distributed robust stabilization problem for networked multi-agent systems with strict negative imaginary uncertainties; (ii) the robust output consensus problem for homogeneous multi-agent systems with negative imaginary dynamics; and (iii) a rendezvous problem for multiple wheeled mobile robots, through the development of cooperative control strategies for integrator negative imaginary systems. The main results of this thesis are summarised as follows. Firstly, a solution to the distributed robust stabilization problem for networked multi-agent systems with strict negative imaginary uncertainties is proposed. The solution includes the derivation of sufficient conditions, in an LMI framework, for the existence of control protocol parameters such that the control protocol robustly stabilizes a networked multi-agent system in presence of strictly negative imaginary uncertainties of certain DC size; and guaranteeing that robust stability is achieved when variations in the network topology occur. Secondly, a solution to the robust output consensus problem for homogeneous multi-agent systems with negative imaginary dynamics is proposed. The solution includes relaxing the assumptions imposed in earlier literature thereby derive robust output consensus conditions under L2 external disturbances and model uncertainty which are not restricted and which simplify in the single-input single-output case to provide several insights not easily captured in the multi-input multi-output case. Finally, a solution to a rendezvous problem for nonholonomic wheeled mobile robots via the negative imaginary systems theory is proposed. The solution includes the derivation of necessary and sufficient conditions that guarantee output consensus and output tracking for strongly connected, balanced and directed networks of integrators subject to energy-bounded disturbances using the negative imaginary internal stability theorems and then utilize the results to achieve rendezvous of multiple wheeled mobile robot. Examples are provided in each of the three aforementioned research problems to demonstrate the effectiveness of the associated proposed results. Additionally, experimental results from real-robots are provided for the rendezvous research problem. This research contributes to the existing literature on cooperative control of multi-agent systems with negative imaginary properties. The research provides a timely and necessary study of the robust stabilization, output consensus and rendezvous problems for networked systems with negative imaginary properties. This current research is important since many practical systems can be modelled as negative imaginary systems and achieving a certain behaviour in multi-agent systems has potential real-world applications.

Systems with a negative imaginary (NI) frequency response for positive frequencies are called NI systems. This property appears in several engineering applications such as nanopositioning systems; gantry crane systems; flexible structures with possibly free body dynamics; hard disk drive servo systems; active filters; descriptor systems and multi-agent networked systems. Particularly, the spillover unmodeled dynamics of flexible structures with collocated position sensors and force actuator have the NI property and controllers based on passivity are inapplicable. Commonly, the unmodeled dynamics are lightly damped, i.e. they are oscillatory. Evidently, there is an interest in designing controllers to reduce the oscillations/vibrations and to guarantee stability against the unmodeled dynamics. Traditional control techniques such as Linear Quadratic Gaussian, H∞ and H₂ may have poor stability margins or may be conservative because of the oscillatory behavior of flexible structures. Interestingly, the positive feedback interconnection of two NI systems is stable if one of them is a subclass of NI, known as weakly strict negative imaginary (WSNI) and also some gain conditions are satisfied. Hence, when the unmodeled dynamics have the NI property, the designed controller should render the nominal closed-loop WSNI and satisfy the gain conditions in order to guarantee stability of the uncertain system. This problem is called the "WSNI synthesis problem". The synthesis of such controller is the main objective of this thesis. Firstly, a set of necessary and sufficient conditions are developed for the characterization of WSNI systems. This result supports both the analysis and synthesis of WSNI systems. Then, a set of sufficient conditions, based on the solution of algebraic Riccati equations (AREs), is provided for the solution of the WSNI synthesis problem. This solution is a dynamic output feedback controller and a formula for such controller is derived. However, the computation of the provided solution is numerically challenging because one of the AREs has a singular Hamiltonian. In order to avoid these numerical challenges, it is necessary to restrict our attention to a subclass of WSNI systems known as strongly strict negative imaginary (SSNI). The problem of synthesizing a controller to render the closed-loop SSNI is called the "SSNI synthesis problem". By investigating further the relations between strict negative imaginary systems and strict positive real systems, it is shown that SSNI systems are equivalent, under a transformation, to classes of SPR systems. Then, necessary and sufficient conditions are developed for the solution of the SSNI synthesis problem. This solution is given in terms of simple linear matrix inequalities (LMIs). These LMIs include the dc value of the closed-loop to guaranteed robust stability of the closed-loop in the negative imaginary framework. Furthermore, a new solution for the SPR synthesis problem is provided, which will be useful when established solutions in the literature for this problem are not feasible. Finally, two numerical examples are given to illustrate the findings and usefulness of the results.

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu's Doctoral thesis, and U-model approach was firstly published in the journal paper titled with 'U-model based pole placement for nonlinear plants' in 2002. The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches. Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems. This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure. With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches. The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm. A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods.

The goal to mitigate the increasing environmental impact of aviation has prompted research into advanced solutions which enable noxious and harmful emissions to be reduced. One of these is represented by aircraft design layouts able to achieve a decrease in aerodynamic drag and aircraft weight, with a tremendous benefit in terms of fuel saving. An important drawback of these configurations (e.g. high aspect ratio and lightweight wings) is their increased flexibility and resulting large deformations, which in turn can drive the aircraft into dangerous instabilities featuring coupling among aerodynamics, structural dynamics and flight dynamics. The discipline addressing the interplay among these different physical mechanisms is called aeroelasticity. Flutter is a dynamic instability in which the aeroelastic coupling is able to produce self-sustained oscillatory motion, and is recognised as a very dangerous and safety-critical phenomenon. The main issues with the established approaches for predicting flutter are the sensitivity to model uncertainties and the difficulty to reliably interpret the effect of nonlinearities on the response of the system. In order to address these challenging aspects, in this thesis techniques from robust control have been explored since this represents a natural setting for providing stability guarantees in the face of uncertainties and nonlinearities, and for constructing models featuring a good trade-off between complexity and reliability. In addition, dynamical systems approaches are investigated because they offer a powerful framework to understand the complex dynamics arising in aeroelastic systems and also observed experimentally. The high-level objective of the thesis is therefore to explore novel approaches to model and analyse aeroelastic systems subject to generic uncertainty and nonlinearities by leveraging the advantages of the above frameworks. Linear methods are first investigated, and original contributions are provided for: construction of Linear Fractional Transformation models; efficient application of μ analysis to the flutter problem; and worst-case performance analysis of Linear Time-Varying systems. In the second part of the thesis, the nonlinear response known as Limit Cycle Oscillation and the closely related problem of determining Region of Attraction have been addressed by proposing novel analysis methodologies which contribute to the state-of-the-art by allowing the effect of uncertainties to be studied. The pursued reconciliation between robust control and dynamic system approaches finally culminates in the proposal of the concept of robust bifurcation margins, which has the potential to extend the use of μ analysis technique to the nonlinear context.

This thesis addresses the design of the atmospheric control system of a launch vehicle. During the ascent-flight phase, the launch vehicle is heavily impacted by wind-induced structural loads and generally exhibits a flexible behaviour characterised by several resonant modes that can generate large oscillations and lead to instability. In this challenging scenario, the control system must ensure stability to guidance commands while satisfying very demanding and tight performance requirements in the presence of parameter dispersions. Based on the above, the atmospheric ascent-flight of a launch vehicle represents a challenging control problem, which is traditionally addressed using a classical design approach. Although there is a rich heritage and experience in applying classical control solutions to the launcher problem, several practical limitations are recognised. With the current industrial state-of-practice it is hard to achieve stability and performance robustness characteristics along the atmospheric phase. In addition, this strategy results in a very time-consuming design, tuning and validation process. Considering the above limitations and also the increasingly competitive launch service market, more methodological synthesis techniques must be proposed to extend the actual control system capabilities as well as to facilitate the control design task. In this context, this thesis proposes a synthesis framework based on robust control techniques. In particular, the capabilities of the structured H∞ and Linear Parameter Varying (LPV) synthesis techniques are explored for the design of the atmospheric control system of the European VEGA launcher. It is shown that these robust control approaches can provide a direct trade-off between robustness versus performance, reduce tuning effort across launch missions and has the capability to simultaneously handle multiple performance requirements and also to explicitly include system uncertainties in the design. This thesis also explores adaptive features for the atmospheric VEGA control system with the aim to evaluate its performance and robustness properties. The main goals of the proposed adaptive scheme are to improve the performance in dispersed conditions and to provide recovery and prevent the loss of the vehicle in extreme off-nominal conditions. Finally, a comparison between the proposed structured H∞, LPV and adaptive controllers are provided.

In recent years, negative imaginary systems have attracted great attention due to their unique properties. The notion of negative imaginary systems was inspired by inertial systems. If a negative imaginary system with a single input and single output is considered, the output of a system follows but lags behind any sinusoidal input to the system by not more than 180 degrees. Additionally, the relative degree of a negative imaginary system is between zero and two. Due to these characterisation of negative imaginary systems, some applications of negative imaginary systems are found in such areas, as large space structures, multi-agent networked systems, and nano-positioning control, etc. In this thesis, some tests are derived to characterise negative imaginary properties. Additionally, internal stability and characterisation of a positive feedback interconnection of negative imaginary systems are also discussed. Firstly, continuous-time and discrete-time negative imaginary lemmas, which are applicable on real, rational, proper negative imaginary systems available in the literature, are derived. These lemmas generalise previous results in order to accommodate negative imaginary systems with possible poles at the origin in continuous-time (respectively poles at z=+1 in discrete-time). The results proposed in these lemmas easily reduce to earlier conditions when the same assumptions are imposed. The introduced necessary and sufficient conditions involving linear matrix inequality conditions give complete state-space characterisation for the full class of real, rational, proper, continuous-time, negative imaginary systems (respectively discrete-time, negative imaginary systems). Moreover, the dimension of the linear matrix inequality Lyapunov variable in these negative imaginary lemmas is smaller than or equal to the McMillan degree of the negative imaginary system. Secondly, a general robust stability theory is formulated to unify all stability results in all theories related to continuous-time negative imaginary systems to date. In the literature, a dc loop gain condition was used to test the internal stability of a positive feedback interconnection of a continuous-time negative imaginary system without poles at the origin and a continuous-time strictly negative imaginary system under instantaneous gain assumptions. By removing these restrictive assumptions that were imposed in prior results, necessary and sufficient conditions are provided for continuous-time negative imaginary systems with poles on imaginary axis, excluding at the origin. The conditions for determining the internal stability of a feedback system directly depend on a mixture of steady-state and infinity gains of the system. On the basis of these stability theorems, general stability results are derived for the case where the most general class of continuous-time negative imaginary systems is interconnected in a feedback system. A key feature for deriving these theorems does not require any complicated matrix factorisations that make the results less intuitive. Additionally, the key stability results easily reduce to the dc loop gain condition under identical assumptions imposed in the literature of continuous-time negative imaginary. Under different but simple assumptions that are not provided in the existing literature, these general stability theorems also simplify to the previous simple condition, i.e., the dc loop gain condition. Specialisations of the general stability theorems under single-input single-output settings are given as corollaries to provide simple but elegant tests for checking feedback stability. Despite the fact that the above theory has been developed in continuous-time, these general robust feedback stability theorems are developed for interconnected discrete-time negative imaginary systems to fill the gap that exists in the literature and these conditions can be considered as discrete-time counterparts of the results that have been obtained in continuous-time. Finally, when a feedback system is considered to be internally stable, continuous-time negative imaginary systems interconnected in a positive feedback have negative imaginary properties. Without imposing the internal stability assumption of the feedback system, necessary and sufficient conditions are derived for a feedback interconnection of continuous-time negative imaginary systems with possible poles at the origin to preserve the characterisation of negative imaginary systems. These results, together with general stability theorems, are applied to check the stability of a string of interconnected continuous-time negative imaginary subsystems. An example in the decentralised control of large vehicle platoons is given to illustrate the usefulness of some of the results in this thesis.

This thesis deals with the topic of min-max formulations of robust model predictive control problems. The sets involved in guaranteeing robust feasibility of the min-max program in the presence of state constraints are of particular interest, and expanding the applicability of well understood solvers of linearly constrained quadratic min-max programs is the main focus. To this end, a generalisation for the set of uncertainty is considered: instead of fixed bounds on the uncertainty, state- and input-dependent bounds are used. To deal with state- and input dependent constraint sets a framework for a particular class of set-valued maps is utilised, namely parametrically convex set-valued maps. Relevant properties and operations are developed to accommodate parametrically convex set-valued maps in the context of robust model predictive control. A quintessential part of this work is the study of fundamental properties of piecewise polyhedral set-valued maps which are parametrically convex, we show that one particular property is that their combinatorial structure is constant. The study of polytopic maps with a rigid combinatorial structure allows the use of an optimisation based approach of robustifying constrained control problems with probabilistic constraints. Auxiliary polytopic constraint sets, used to replace probabilistic constraints by deterministic ones, can be optimised to minimise the conservatism introduced while guaranteeing constraint satisfaction of the original probabilistic constraint. We furthermore study the behaviour of the maximal robust positive invariant set for the case of scaled uncertainty and show that this set is continuously polytopic up to a critical scaling factor, which we can approximate a-priori with an arbitrary degree of accuracy. Relevant theoretical statements are developed, discussed and illustrated with examples.

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems.

Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state. To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques. Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size. The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible' sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.

The study of non-linear input-output maps can be summarized by three concepts: Gain, Positivity and Dissipativity. However, in order to make efficient use of these theorems it is necessary to use loop transformations and weightings, or so called ”multipliers”.The first problem this thesis studies is the feedback interconnection of a Linear Time Invariant system with a memoryless bounded and monotone non-linearity, or so called Absolute Stability problem, for which the test for stability is equivalent to show the existence of a Zames-Falb multiplier. The main advantage of this approach is that Zames–Falb multipliers can be specialized to recover important tools such as Circle criterion and the Popov criterion. Albeit Zames-Falb multipliers are an efficient way of describing non-linearities in frequency domain, the Fourier transform of the multiplier does not preserve the L1 norm. This problem has been addressed by two paradigms: mathematically complex multipliers with exact L1 norm and multipliers with mathematically tractable frequency domain properties but approximate L1 norm. However, this thesis exposes a third factor that leads to conservative results: causality of Zames-Falb multipliers. This thesis exposes the consequences of narrowing the search Zames-Falb multipliers to causal multipliers, and motivated by this argument, introduces an anticausal complementary method for the causal multiplier synthesis in [1].The second subject of this thesis is the feedback interconnection of two bounded systems. The interconnection of two arbitrary systems has been a well understood problem from the point of view of Dissipativity and Passivity. Nonetheless, frequency domain analysis is largely restricted for passive systems by the need of canonically factorizable multipliers, while Dissipativity mostly exploits constant multipliers. This thesis uses IQC to show the stability of the feedback interconnection of two non-linear systems by introducing an equivalent representation of the IQC Theorem, and then studies formally the conditions that the IQC multipliers need. The result of this analysis is then compared with Passivity and Dissipativity by a series of corollaries.

Robust control is an aspect of control theory which explicitly considers uncertainties and how they affect robust stability in the analysis and design of control decisions. A basic requirement for optimal robust guaranteed control in a real life scenario is the stabilization of systems in the presence of uncertainties or perturbations. In this thesis, the system uncertainties are embedded into a norm bounded uncertainty elements. The perturbation function is modelled as a class of nonlinear uncertainty influencing a neutral system with infinite delay. It is assumed to have delay in state and is input dependent; which implies the effect of control action can directly or indirectly influence the nonlinear perturbation function. In recognition of the fact that stability and controllability are fundamental in obtaining the optimal robust guaranteed cost control design for neutral functional integro-differential systems with infinite delays (NFDSID), total asymptotic stability results were developed using Razumikhin technique, unique properties of eigenvalues, and the uniform stability properties of the functional difference operator for neutral systems. The new results, obtained using Razumikhin’s technique, extend and complement basic stability results in neutral systems to NFDSID. Novel sufficient conditions were developed for the null controllability of nonlinear NFDSID when the controls are constrained. By exploring the knowledge gained through other controllability results; conditions are placed on the perturbation function. This guaranteed that, if the uncontrolled system is uniformly asymptotically stable, and the controlled system satisfies a full rank condition, then the control system is null controllable with constraint if it satisfies some algebraic conditions. The investigation of optimal robust guaranteed cost control method has resulted in a novel delay dependent stability criterion for a nonlinear NFDSID with a given quadratic cost function. The new design is based on a model transformation technique, Lyapunov matrix equation and Lyapunov-Razumikhin stability approach. The Lyapunov-Razumikhin technique is adopted for this investigation because it is considered more scalable for optimal robust guaranteed cost control design for NFDSID. It is demonstrated that a memory less feedback control can be synthesized appropriately to ensure: (i) the closed-loop systems robust stability, and (ii) guarantee that the closed-loop cost function value remains within a specified bound. The problem of designing the optimal guaranteed cost controller is also realized in terms of inequalities. The Lyapunov-Krasovskii method is used to obtain stability conditions in comparison to the Razumikhin method. This method leads to linear matrix inequality (LMI) for the delay-independent case which is known to be conservative. To illustrate the potential practical applicability of the theoretical results; a cascade connection of two fully filled chemical solution mixers, and an integrated lossless transmission line which has a capacitance, inductance, resistance and terminated by a nonlinear function are modelled. A neutral control system model for NFDSID is derived from each of these systems. Simulation studies on the transmission line system confirm the theoretical robust stability results. The new results and methods of analysis expounded in this thesis are explicit, computationally more effective than existing ones and will serve as a working document for the present and future generations in the comity of researchers and industries alike.

A robust model predictive control algorithm is presented that explicitly handles multiplicative, or parametric, uncertainty in linear discrete models over a finite horizon. The uncertainty in the predicted future states and inputs is bounded by polytopes. The computational cost of running the controller is reduced by calculating matrices offline that provide a means to construct outer approximations to robust constraints to be applied online. The robust algorithm is extended to problems of uncertain models with an allowed probability of violation of constraints. The probabilistic degrees of satisfaction are approximated by one-step ahead sampling, with a greedy solution to the resulting mixed integer problem. An algorithm is given to enlarge a robustly invariant terminal set to exploit the probabilistic constraints. Exponential basis functions are used to create a Robust MPC algorithm for which the predictions are defined over the infinite horizon. The control degrees of freedom are weights that define the bounds on the state and input uncertainty when multiplied by the basis functions. The controller handles multiplicative and additive uncertainty. Robust MPC is applied to the problem of wind turbine control. Rotor speed and tower oscillations are controlled by a low sample rate robust predictive controller. The prediction model has multiplicative and additive uncertainty due to the uncertainty in short-term future wind speeds and in model linearisation. Robust MPC is compared to nominal MPC by means of a high-fidelity numerical simulation of a wind turbine under the two controllers in a wide range of simulated wind conditions.

The presence of uncertainty in model predictive control (MPC) has been accounted for using two types of approaches: robust MPC (RMPC) and stochastic MPC (SMPC). Ideal RMPC and SMPC formulations consider closed-loop optimal control problems whose exact solution, via dynamic programming, is intractable for most systems. Much effort then has been devoted to find good compromises between the degree of optimality and computational tractability. This thesis expands on this effort and presents robust and stochastic MPC strategies with reduced online computational requirements where the conservativeness incurred is made as small as conveniently possible. Two RMPC strategies are proposed for linear systems under additive uncertainty. They are based on a recently proposed approach which uses a triangular prediction structure and a non-linear control policy. One strategy considers a transference of part of the computation of the control policy to an offline stage. The other strategy considers a modification of the prediction structure so that it has a striped structure and the disturbance compensation extends throughout an infinite horizon. An RMPC strategy for linear systems with additive and multiplicative uncertainty is also presented. It considers polytopic dynamics that are designed so as to maximize the volume of an invariant ellipsoid, and are used in a dual-mode prediction scheme where constraint satisfaction is ensured by an approach based on a variation of Farkas' Lemma. Finally, two SMPC strategies for linear systems with additive uncertainty are presented, which use an affine-in-the-disturbances control policy with a striped structure. One strategy considers an offline sequential design of the gains of the control policy, while these are variables in the online optimization in the other. Control theoretic properties, such as recursive feasibility and stability, are studied for all the proposed strategies. Numerical comparisons show that the proposed algorithms can provide a convenient compromise in terms of computational demands and control authority.

With the growth in requirement for a high reliability of power supply, stability of the power system and the minimum requirement for control systems becomes more and more significant. The most popular way to solve the problem of stability is to install power system stabilizers (PSSs) on synchronous generators in related power systems. The conventional methods for designing PSS are generally based on the compensation approach for the phase and eigenvalue of the generator model. In recent decades, H-norm based robust PSS has been developed because of the system uncertainty of power grids. In another aspect, wind power has evolved into a significant renewable energy source and increased at an outstanding rate. Stability problems of power system with large wind farms became more and more challenging. Some wind plant modelling methods, for which PS Ss are not taken into consideration, have been developed and widely used in practical applications. The present study is concerned with a comprehensive power system stability analysis based on an improved H-nOl'ffi robust controller design method and a novel modelling approach for doubly fed induction generator (DFIG) wind turbines. Initially, one improved lemma, enhanced with LMI regional pole placement, is developed for linear matrix inequality eLMI) based H2/Hoo robust output feedback controller design. Robust PS Ss are designed based on the approach and they are tested in both single and multimachine systems. A novel DFIG wind turbine model is then built up and tested with the robust PSS in both single and multi-machine systems to see the oscillations damping ability. Finally, based on the robust PSS, a large multi-machine power system with wind parks is selected for a comprehensive stability analysis. Simulated examples and case studies are employed in this study to demonstrate the effect of new PS Ss. The simulation results clearly suggest that the proposed PSS can solve the stability problem of damping oscillations in power systems with large wind parks.

Solar Wireless Networked Control Systems (SWNCS) are a style of distributed control systems where sensors, actuators, and controllers are interconnected via a wireless communication network. This system setup has the benefit of low cost, flexibility, low weight, no wiring and simplicity of system diagnoses and maintenance. However, it also unavoidably calls some wireless network time delays and packet dropout into the design procedure. Solar lighting system offers a clean environment, therefore able to continue for a long period. SWNCS also offers multi Service infrastructure solution for both developed and undeveloped countries. The system provides wireless controller lighting, wireless communications network (WI-FI/WIMAX), CCTV surveillance, and wireless sensor for weather measurement which are all powered by solar energy.

In nature, through millions of years of evolution, fish and cetaceans have developed fast efficient and highly manoeuvrable methods of marine propulsion. A recent explosion in demand for sub sea robotics, for conducting tasks such as sub sea exploration and survey has left developers desiring to capture some of the novel mechanisms evolved by fish and cetaceans to increase the efficiency of speed and manoeuvrability of sub sea robots. Research has revealed that interactions with vortices and other unsteady fluid effects play a significant role in the efficiency of fish and cetaceans. However attempts to duplicate this with robotic fish have been limited by the difficulty of predicting or sensing such uncertain fluid effects. This study aims to develop a gait generation method for a robotic fish with a degree of passivity which could allow the body to dynamically interact with and potentially synchronise with vortices within the flow without the need to actually sense them. In this study this is achieved through the development of a novel energy based gait generation tactic, where the gait of the robotic fish is determined through regulation of the state energy rather than absolute state position. Rather than treating fluid interactions as undesirable disturbances and `fighting' them to maintain a rigid geometric defined gait, energy based control allows the disturbances to the system generated by vortices in the surrounding flow to contribute to the energy of the system and hence the dynamic motion. Three different energy controllers are presented within this thesis, a deadbeat energy controller equivalent to an analytically optimised model predictive controller, a $H_\infty$ disturbance rejecting controller with a novel gradient decent optimisation and finally a error feedback controller with a novel alternative error metric. The controllers were tested on a robotic fish simulation platform developed within this project. The simulation platform consisted of the solution of a series of ordinary differential equations for solid body dynamics coupled with a finite element incompressible fluid dynamic simulation of the surrounding flow. results demonstrated the effectiveness of the energy based control approach and illustrate the importance of choice of controller in performance.

Variable Horizon Model Predictive Control (VH-MPC) is a form of predictive control that includes the horizon length as a decision variable in the constrained optimisation problem solved at each iteration. It has been recently applied to completion problems, where the system state is to be steered to a closed set in finite time. The behaviour of the system once completion has occurred is not considered part of the control problem. This thesis is concerned with three aspects of robustness and optimality in VH-MPC completion problems. In particular, the thesis investigates robustness to well defined but unpredictable changes in system and controller parameters, robustness to bounded disturbances in the presence of certain input parameterisations to reduce computational complexity, and optimal robustness to bounded disturbances using tightened constraints. In the context of linear time invariant systems, new theoretical contributions and algorithms are developed. Firstly, changing dynamics, constraints and control objectives are addressed by introducing the notion of feasible contingencies. A novel algorithm is proposed that introduces extra prediction variables to ensure that anticipated new control objectives are always feasible, under changed system parameters. In addition, a modified constraint tightening formulation is introduced to provide robust completion in the presence of bounded disturbances. Different contingency scenarios are presented and numerical simulations demonstrate the formulation’s efficacy. Next, complexity reduction is considered, using a form of input parameterisation known as move blocking. After introducing a new notation for move blocking, algorithms are presented for designing a move-blocked VH-MPC controller. Constraints are tightened in a novel way for robustness, whilst ensuring that guarantees of recursive feasibility and finite-time completion are preserved. Simulations are used to illustrate the effect of an example blocking scheme on computation time, closed-loop cost, control inputs and state trajectories. Attention is now turned towards mitigating the effect of constraint tightening policies on a VH-MPC controller’s region of attraction. An optimisation problem is formulated to maximise the volume of an inner approximation to the region of attraction, parameterised in terms of the tightening policy. Alternative heuristic approaches are also proposed to deal with high state dimensions. Numerical examples show that the new technique produces substantially improved regions of attraction in comparison to other proposed approaches, and greatly reduces the maximum required prediction horizon length for a given application. Finally, a case study is presented to illustrate the application of the new theory developed in this thesis to a non-trivial example system. A simplified nonlinear surface excavation machine and material model is developed for this purpose. The model is stabilised with an inner-loop controller, following which a VH-MPC controller for autonomous trajectory generation is designed using a discretised, linearised model of the stabilised system. Realistic simulated trajectories are obtained from applying the controller to the stabilised system and incorporating the ideas developed in this thesis. These ideas improve the applicability and computational tractability of VH-MPC, for both traditional applications as well as those that go beyond the realm of vehicle manœuvring.

This thesis is concerned with the choice of the uncertainty structure in robust control problems. This choice affects the optimization carried out to obtain a robust feedback controller, and determines how robust a feedback loop will be to discrepancies in the parameters or dynamics of the plant model. Firstly, it presents readily applicable distance measures, robust stability margins and associated robust stability and robust performance theorems for several commonly used uncertainty structures for linear time-invariant systems (additive, multiplicative, inverse multiplicative, inverse additive, right coprime factor uncertainty).Secondly, the thesis discusses the robust stabilization problem for linear plants with a coprime factor uncertainty structure where the coprime factors of the plant are not necessarily normalized. The problem considered here is a generalization of the normalized coprime factor robust stabilization problem. It is shown that the minimum of the ratio of (non-normalized) coprime factor distance over (non-normalized) coprime factor robust stability margin, termed the robustness ratio, is an important bound in robust stability and performance results. A synthesis method is proposed which maintains a lower bound on the normalized coprimefactor robust stability margin (as a proxy for nominal performance) while also robustly stabilizing a particular perturbed plant, potentially far outside a normalized coprime factor neighbourhood of the nominal plant. The coprime factor synthesis problem is also considered in a state-space framework. It is shown that it admits a simple and intuitive controller implementation in observer form. Via the solution of one Riccati equation, an optimally robust observer gain L can be obtained for any state-feedback matrix F. One particular method for obtaining a suitable F is also proposed, ensuring that the feedback loop is particularly robust to uncertain lightly damped poles and zeros.

The primary objective of this thesis is to leverage on the framework of H∞ loop-shaping control to formulate efficient and powerful optimization algorithms in LMI framework for the synthesis of performance loop-shaping weights. The H∞ loop-shaping design procedure is an efficient controller synthesis technique that combines classical loop-shaping concepts with H∞ synthesis. This procedure establishes a good tradeoff between robust stability and robust performance of a closed-loop system in a systematic manner. However, the selection of pre- and/or post-compensators, a crucial step in the design procedure, is nontrivial as factors such as the right half plane poles/zeros of the nominal plant, roll-off rate around the crossover frequency, strength of cross-coupling in multi-input multi-output systems, expected bandwidth, etc. must be adequately considered.Firstly, a frequency-dependent weight optimization framework is formulated in state-space form in order to remove the dependency on frequency while retaining the objective of maximizing the robust stability margin of a closed-loop system. This formulation facilitates the synthesis of low-order controllers, which is desirable from an implementation perspective.A weight optimization framework that incorporates smoothness constraints in order to prevent the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, is subsequently formulated. The proposed formulation is intuitive from a design perspective as the smoothness constraints are expressed as gradient constraints on a log-log scale in dB/decade, consistent with the notation used in Bode plot for single-input single-output systems and singular value plots for multi-input multi-output systems.Thereafter, an optimization framework that maximizes the robust performance of a closed-loop system is presented. The philosophy in this framework is in line with practical design objectives that give the best achievable robust performance on a particular problem once a level of robust stability margin is demanded.Lastly, a novel unmanned vehicle is proposed. The vehicle uses a full six-degree-of-freedom tri-rotor actuation, capable of fully decoupled thrust and torque vectoring in all the 3D space. This vehicle can act as an unmanned ground vehicle or unmanned aerial vehicle, but the objective herein is restricted to the upright stability of the vehicle while operating on the ground as this is a precursor to rolling motion. The full nonlinear model of the vehicle is derived and linearized for subsequent controller synthesis, and this is thereafter validated by means of numerical simulations.

In the thesis, two different model predictive control (MPC) strategies are investigated for linear systems with uncertainty in the presence of constraints: namely robust MPC and stochastic MPC. Firstly, a Youla Parameter is integrated into an efficient robust MPC algorithm. It is demonstrated that even in the constrained cases, the use of the Youla Parameter can desensitize the costs to the effect of uncertainty while not affecting the nominal performance, and hence it strengthens the robustness of the MPC strategy. Since the controller u = K x + c can offer many advantages and is used across the thesis, the work provides two solutions to the problem when the unconstrained nominal LQ-optimal feedback K cannot stabilise the whole class of system models. The work develops two stochastic tube approaches to account for probabilistic constraints. By using a semi closed-loop paradigm, the nominal and the error dynamics are analyzed separately, and this makes it possible to compute the tube scalings offline. First, ellipsoidal tubes are considered. The evolution for the tube scalings is simplified to be affine and using Markov Chain model, the probabilistic tube scalings can be calculated to tighten the constraints on the nominal. The online algorithm can be formulated into a quadratic programming (QP) problem and the MPC strategy is closed-loop stable. Following that, a direct way to compute the tube scalings is studied. It makes use of the information on the distribution of the uncertainty explicitly. The tubes do not take a particular shape but are defined implicitly by tightened constraints. This stochastic MPC strategy leads to a non-conservative performance in the sense that the probability of constraint violation can be as large as is allowed. It also ensures the recursive feasibility and closed-loop stability, and is extended to the output feedback case.

This thesis presents alternative methods for designing a speed controller for a hydrostatic power transmission system. Recognising that such a system, comprising a valve controlled motor supplied by the laboratory ring main and driving a hydraulic pump as a load, contains significant non-linearities, the thesis shows that robust 'modern control' approaches may be applied to produce viable controllers without recourse to the use of a detailed model of the system. In its introduction, it considers why similar approaches to the design of fluid power systems have not been applied hitherto. It then sets out the design and test, in simulation and on a physical rig, of two alternative linear controllers using H∞ based methods and a 'self organising fuzzy logic' controller (SOFLC). In the linear approaches, differences between the characteristics of the system and the simple models of it are accommodated in the controller design route as 'perturbations' or 'uncertainties'. The H∞ based optimisation methods allow these to be recognised in the design. “Mixed sensitivity” and “Loop shaping” methods are each applied to design controllers which are tested successfully on the laboratory rig. The SOFLC in operation does not rely on a model, but instead allows fuzzy control rules to evolve. In the practical tests, the system is subjected to a range of disturbances in the form of supply pressure fluctuations and load torque changes. Also presented are test results for proportional and proportional plus integral (PI) controllers, to provide a reference. It is demonstrated qualitatively that performance using the linear controllers is superior to that using proportional and PI controllers. An increased range of stable operation is achieved by the controller designed using “loop shaping” – performance is enhanced by the use of two controllers selected automatically according to the operating speed, using a “bumpless” transfer routine. The SOFLC proved difficult to tune. However, stable operation was achieved.

New technological advances and the requirements to increasingly abide by new safety laws in engineering design projects highly affects industrial products in areas such as automotive, aerospace and railway industries. The necessity arises to design reduced-cost hi-tech products with minimal complexity, optimal performance, effective parameter robustness properties, and high reliability with fault tolerance. In this context the control system design plays an important role and the impact is crucial relative to the level of cost efficiency of a product. Measurement of required information for the operation of the design control system in any product is a vital issue, and in such cases a number of sensors can be available to select from in order to achieve the desired system properties. However, for a complex engineering system a manual procedure to select the best sensor set subject to the desired system properties can be very complicated, time consuming or even impossible to achieve. This is more evident in the case of large number of sensors and the requirement to comply with optimum performance. The thesis describes a comprehensive study of sensor selection for control and fault tolerance with the particular application of an ElectroMagnetic Levitation system (being an unstable, nonlinear, safety-critical system with non-trivial control performance requirements). The particular aim of the presented work is to identify effective sensor selection frameworks subject to given system properties for controlling (with a level of fault tolerance) the MagLev suspension system. A particular objective of the work is to identify the minimum possible sensors that can be used to cover multiple sensor faults, while maintaining optimum performance with the remaining sensors. The tools employed combine modern control strategies and multiobjective constraint optimisation (for tuning purposes) methods. An important part of the work is the design and construction of a 25kg MagLev suspension to be used for experimental verification of the proposed sensor selection frameworks.

In this thesis we develop performance bounds for adaptive control designs applicable to functionally uncertain systems in either the affine, strict feedback and output feedback normal forms. L², weighted L², L∞ and weighted L∞ models of uncertainty are introduced. These allow us to specify the uncertainty in the system independently of the model structure chosen for the adaptive controller. A modified LQR cost functional, incorporating both control effort and state terms, is introduced and its interpretation is discussed. The main results bound this cost functional in terms of the uncertainty models for a class of Lyapunov based adaptive controllers. One class of results shows that a finite dimensional model suffices for stabilization given a sufficiently large adaptation gain. A second class of results considers global uncertainties. It is shown that unless the adaptation rate is faster than the uncertainty growth, instability may occur. An unbounded adaptive rate structure is described which allows global results to be given, using a special class of physically realisable global models, under the assumption that the uncertainty growth is known, but not the uncertainty level. An example is given of a standard spline network based controller whose performance degrades as the resolution of the model increases. We then give a sufficient condition on the model for the performance to be asymptotically bounded independent of the size of the model. Under further L∞ assumptions on the uncertainty model, we construct a control schema which has the required performance scalability. It is argued that average case performance costs are more natural than worst case costs for the adaptive designs, and it is shown how the average case performance costs can be estimated from the worst case bounds. The open problem of a structurally adaptive scheme which is stable in the absence of smoothness information is also solved.