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In networked control systems, the communication load is a main concern for implementing model predictive control (MPC). This paper introduces a self-triggered MPC algorithm under network environments to reduce communication load, for discrete-time linear systems with bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly based on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered model predictive control of a nominal system. Moreover, the new cost function explicitly adopts communication load is in consideration. The proposed algorithm is proved to drive the system to an invariant set with respect to the bounded disturbances. Finally, simulation results is provided to verify the effectiveness of the proposed robust output feedback MPC algorithm. [ABSTRACT FROM AUTHOR]

Quantisation is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantised observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantised realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a $ \ell _{p},(0 \lt p \lt 1), $ ℓ p , (0 < p < 1) , quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the $ \ell _{1} $ ℓ 1 minimisation in terms of the sparsity of the induced solution. [ABSTRACT FROM AUTHOR]

Stability analysis is the most basic and important problem of dynamic systems, which has been extensively studied in the last few decades. The research on finite-time stability and stability in distribution of k-valued logical networks (KVLNs) with Markov jump disturbances (MJDs) is considered in this paper. To begin with, we establish an equivalent Markov jump system for the considered KVLNs with MJDs via semi-tensor product (STP) of matrices, which can simplify the stability analysis of KVLNs with MJDs. Next, two criteria are proposed for finite-time stability and stability in distribution of KVLNs with MJDs, respectively. At last, the validity of the obtained results is illustrated by simulation on the apoptosis network. [ABSTRACT FROM AUTHOR]

The output feedback robust model predictive control (MPC) for the linear systems with norm-bounded uncertainty and disturbance is studied. A new state estimator is formulated where both estimator dynamic matrix and estimator gain are decision variables being optimised on-line. The infinite horizon control moves are parameterised as a feedback control law, and the resultant non-convex optimisation problem is solved through a linearisation method. The recursive feasibility and closed-loop stability are guaranteed. The proposed approach can achieve better performance and include previous approaches as special cases. Two numerical examples are given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Manifold consensus in the multi-objective sense of frequency synchronism, torque angle specification, power swing reduction, and inter-generator dynamics decoupling in multi-machine power systems is addressed, via the augmented multi-agent collision control. Firstly with respect to a multi-machine power system, the manifold consensus is re-formulated as a specific multi-agent flocking collision in the mirrored multi-agent network with augmented-dimension nodes representing the generators and excitation systems (ES). Secondly, by forcing the multi-agents into flocking collision under virtual controls, according to which the control actions of ES are determined so that all generators achieve the multiple objectives simultaneously. Thirdly, distributed implementation by partial multi-agent networking is explained. Finally, numerical examples are included to illustrate the techniques. Advantages include: multi-objective control in multi-machine power networks is achievable, independent of the Lyapunov theory; controller parametrization is numerically tractable and with more freedoms, involving no generator and ES dynamical models; implementation can be across the whole network or its partial subsystems. [ABSTRACT FROM AUTHOR]

A method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers was recently proposed by introducing an additional controlled variable, viz., the signed area of a triangle. In this paper, we seek to generalise this method to planar formations of n agents for both first- and second-order agent models while using unidirectional sensing and control. In addition to directed formation shape control, we also consider the problem of formation motions. We prove that, under certain conditions on the edge lengths of the triangulated desired formation and control gains, the distributed controller ensures the almost-global asymptotic stability of the correct formation and is coordinate frame invariant. Experimental evaluations are presented to support the theoretical results. [ABSTRACT FROM AUTHOR]

Sliding mode quantisers (SMQs), where signals are converted to switching signals represented by the sequence of binary values − 1 's and + 1 's, are increasingly being used in various applications including control of power converters, networked control systems (NCSs), one-bit control processing, etc. This paper derives the stability conditions of nonlinear control system embedded with SMQ-based Δ-M. The equivalence conditions of the proposed SMQ, which assure that its binary outputs are equivalent to its inputs, are established. The results of theoretical analysis are validated through simulation considering an example of the underwater vehicle control system, where the transmission bit-rate is limited by 100 b / s . The results of the simulation demonstrates that the quantised feedback signals effectively control the system and achieves both the desired specifications and the bandwidth reduction. [ABSTRACT FROM AUTHOR]

A new elementary operation approach (NEOA) for Roesser model realisation of multi-input and multi-output (MIMO) multidimensional (n-D) systems has been recently proposed, which can generate a lowest possible realisation but requires trying different processing manners for various possible realisations with different structures and orders. This paper develops two kinds of novel order evaluation methods and the corresponding algorithms for the realisation procedures A and B of the NEOA, respectively, such that the best processing manner for the lowest possible realisation can be determined with much less computational complexity. These new results enable us, for the first time, to know exactly the order of a realisation before actually conducting the realisation, and thus provide us a novel and high-efficiency way to explore the lowest possible realisation problem for MIMO n-D systems. Examples are given throughout this paper to illustrate the main idea as well as effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Piecewise affine systems constitute a popular framework for the approximation of non-linear systems and the modelling of hybrid systems. This paper addresses the recursive subsystem estimation in continuous-time piecewise affine systems. Parameter identifiers are extended from continuous-time state-space models to piecewise linear and piecewise affine systems. The convergence rate of the presented identifiers is improved further using concurrent learning, which makes concurrent use of current and recorded measurements. In concurrent learning, assumptions on persistence of excitation are replaced by the less restrictive linear independence of the recorded data. The introduction of memory, however, reduces the tracking ability of concurrent learning because errors in the recorded measurements prevent convergence to the true parameters. In order to overcome this limitation, an algorithm is proposed to detect and remove erroneous measurements at run-time and thereby restore the tracking ability. Detailed examples are included to validate the proposed methods numerically. [ABSTRACT FROM AUTHOR]

This paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included. [ABSTRACT FROM AUTHOR]

Improving the robustness, vis-à-vis matched input disturbances of interconnection and damping assignment, passivity based control (IDA-PBC) for a class of underactuated mechanical systems is addressed in this paper. The characterised class of systems is described by a Port Controlled Hamiltonian (PCH) model which represents another alternative to the classical Euler-Lagrange models for which IDA-PBC yields a smooth stabilising controller. Our main contribution consists of combining the so-called IDA-PBC controller with an adaptive control technique. Some sufficient stability conditions on matched input disturbances are given. In order to estimate the stability and performance robustness of both controllers, a stochastic robustness analysis was used. Indeed, we used the Monte Carlo simulation (MCS) based on uncertainties to analyse the behaviour of the closed-loop system. The comparison of the stability robustness between the classical IDA-PBC controller and the proposed one is then provided. As an illustration, we proposed to revisit the application of IDA-PBC controller to the inertia wheel inverted pendulum in the presence of matched disturbances. Simulation and real-time experimental results mirror the theoretical results and prove the efficiency of the proposed controller. [ABSTRACT FROM AUTHOR]

In recent years, delta (Δ-M) and delta-sigma modulators (ΔΣ-M) are increasingly being used as efficient data converters due to numerous advantages they offer. This paper investigates various dynamical features of these modulators/systems (both in continuous and discrete time domain) and derives their stability conditions using the theory of sliding mode. The upper bound of the hitting time (step) has been estimated. The equivalent mode conditions, i.e. where the outputs of the modulators are equivalent to the inputs, are established. The results of the analysis are validated through simulations considering a numerical example. [ABSTRACT FROM AUTHOR]

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we design a controller for stabilising a control system. The technique used for designing the controller includes a linear regulator and an asymptotical observer which form the controller. The linear regulator designed is a feedback of estimated states and also it must minimise a quadratic performance index. The gain matrix of optimal feedback is obtained by solving the Riccati equation, whilst the gain observer matrix is computed by making use of symmetrical systems properties. The properties of symmetrical systems allow us to find the optimal gain matrix of the observer without solving the dual Riccati equation, we only need to compute the matrices of controllability and observability. Having calculated the gain matrices of regulator and of observer, we proceeded to compute the transfer function of the observer-based controller. [ABSTRACT FROM AUTHOR]

The output feedback robust model predictive control (MPC), for the linear parameter varying (LPV) system with norm-bounded disturbance, is addressed, where the model parametric matrices are only known to be bounded within a polytope. The previous techniques of norm-bounding technique, quadratic boundedness (QB), dynamic output feedback, and ellipsoid (true-state bound; TSB) refreshment formula for guaranteeing recursive feasibility, are fused into the newly proposed approaches. In the notion of QB, the full Lyapunov matrix is applied for the first time in this context. The single-step dynamic output feedback robust MPC, where the infinite-horizon control moves are parameterised as a dynamic output feedback law, is the main topic of this paper, while the multi-step method is also suggested. In order to strictly guarantee the physical constraints, the outer bound of the true state replaces the true state itself, so tightness of this bound has a major effect on the control performance. In order to tighten the TSB, a procedure for refreshing the real-time ellipsoid based on that of the last sampling instant is given. This paper is conclusive for the past results and far-reaching for the future researches. Two benchmark examples are given to show the effectiveness of the novel results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of global stabilisation of a class of generalised cascaded systems. By using the extended adding a power integrator technique, a global controller is first constructed for the driving subsystem. Then based on the homogeneous properties and polynomial assumption, it is shown that the stabilisation of the driving subsystem implies the stabilisation of the overall cascaded system. Meanwhile, by properly choosing some control parameters, the global finite-time stability of the closed-loop cascaded system is also established. The proposed control method has several new features. First, the nonlinear cascaded systems considered in the paper are more general than the conventional ones, since the powers in the nominal part of the driving subsystem are not required to be restricted to ratios of positive odd numbers. Second, the proposed method has some flexible parameters which provide the possibility for designing continuously differentiable controllers for cascaded systems, while the existing designed controllers for such kind of cascaded systems are only continuous. Third, the homogenous and polynomial conditions adopted for the driven subsystem are easier to verify when compared with the matching conditions that are widely used previously. Furthermore, the efficiency of the proposed control method is validated by its application to finite-time tracking control of non-holonomic wheeled mobile robot. [ABSTRACT FROM AUTHOR]

Total energy shaping is a controller design methodology that achieves (asymptotic) stabilisation of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function. The success of the method relies on the possibility of solving two partial differential equations (PDEs) which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the PDE associated to the kinetic energy (KE) which is quasi-linear and non-homogeneous, and the solution that defines the desired inertia matrix must be positive definite. This task is simplified by the inclusion of gyroscopic forces in the target dynamics, which translates into the presence of a free skew-symmetric matrix in the KE matching equation that reduces the number of PDEs to be solved. Recently, it has been claimed that considering a more general form for the target dynamic forces that relax the skew-symmetry condition further reduces the number of KE PDEs. The purpose of this paper is to prove that this claim is wrong. [ABSTRACT FROM PUBLISHER]

In this work, an adaptive iterative learning control (AILC) scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time-varying delays and input saturations. By incorporating a saturation function, a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain, which is used to estimate the unknown time-varying system uncertainty. A new time-weighted Lyapunov–Krasovskii-like composite energy function (LKL-CEF) is designed for the convergence analysis where time-weighted inputs, states and estimates of system uncertainty are all considered. Despite the existence of time-varying parametric uncertainties, time-varying delays, input saturations and localLipschitznonlinearities, the learning convergence is guaranteed with rigorous mathematical analysis. Simulation results verify the correctness and effectiveness of the proposed method further. [ABSTRACT FROM PUBLISHER]

In this paper, the enclosing control problem of second-order multi-agent systems is considered, where the targets can be either stationary or moving. The objective is to achieve an equidistant circular formation for a group of agents to enclose a team of targets. In order to do so, we first introduce a formal definition explaining certain basic properties of the exploring relation between the agents and the targets. We then construct the estimator of the centre of the targets, which is used to build the control protocol to achieve equidistant circular enclosing. Using a Lyapunov function and Lasalle’s Invariance Principle, the convergency of the estimator and control protocol are, respectively, established. We then construct a smooth function to approximate the discontinuous term in the estimator. Finally, the simulations for stationary targets and moving targets are given to verify the validity of the results obtained. [ABSTRACT FROM AUTHOR]

We formulate a matrix interpolation problem with existing interpolation points on the imaginary axis and infinity and existing equal left and right interpolation points, using the concept of parametrisation of stabilising controllers. Then, we solve the problem of obtaining all its solutions. If interpolation points at infinity are absent, we show that the introduced problem is equivalent to the existing one. We apply this result to solve the problem of optimal interpolation with existent interpolation points on the imaginary axis and infinity. We show by an example that the solution of optimal interpolation is directly applicable to the one-blockoptimal control with existent invariant zeros on the imaginary axis and infinity. It is seen from the example that not only the transfer matrix of the closed-loop system is constrained on the extended imaginary axis, but also its derivatives. [ABSTRACT FROM AUTHOR]

This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances. [ABSTRACT FROM AUTHOR]

This paper addresses multi-agent control under an environment where both agent-to-agent communication and one-to-all broadcast are available. The problem studied here is a consensus problem for a pre-specified location, i.e. collecting the agents at a desired location in ann-dimensional space, with a limited communication range and an unlimited broadcast range, which is a nice example to be solved under the mixed environment. For solving this, we first introduce a concept of the connected agent group. Using this notion, the problem is reduced to a consensus problem for the group-to-group relation and that for the agent-to-agent relation in the groups, from which we derive a controller achieving the consensus with probability 1. Finally, the performance of the proposed controller is demonstrated by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper characterises stochastic convergence properties of adjoint-based (gradient-based) iterative learning control (ILC) applied to systems with load disturbances, when provided only with approximate gradient information and noisy measurements. Specifically, conditions are discussed under which the approximations will result in a scheme which converges to an optimal control input. Both the cases of time-invariant step sizes and cases of decreasing step sizes (as in stochastic approximation) are discussed. These theoretical results are supplemented with an application on a sequencing batch reactor for wastewater treatment plants, where approximate gradient information is available. It is found that for such case adjoint-based ILC outperforms inverse-based ILC and model-free P-type ILC, both in terms of convergence rate and measurement noise tolerance. [ABSTRACT FROM PUBLISHER]

We consider an average consensus problem for multi-agent systems based on a two-layer hierarchical cyclic pursuit update scheme in discrete time. The aim is to achieve a faster rate of convergence and in particular to minimise the size of the dominating eigenvalue of the system. This is done by finding (i) the appropriate grouping for the given number of agents and then (ii) the optimal weights to be employed in the update scheme of each agent. The underlying graph structure is directed, and hence the problem is non-convex. We provide a general solution for this problem, which indicates that conventional weights are optimal only in certain cases. Numerical examples are given to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This article extends the concept of input-output finite time stability (IO-FTS) to a class of hybrid systems, namely impulsive dynamical linear systems, which are systems that exhibit jumps in the state trajectory. Sufficient conditions are given for the analysis of IO-FTS and for the design of both static output and state feedback controllers, guaranteeing IO-FTS of the closed loop system. In the general case the presented results require to solve feasibility problems involving either linear matrix inequalities or bilinear matrix inequalities, which can be solved numerically in an efficient way by using off-the-shelf optimisation tools, as illustrated by the proposed examples. [ABSTRACT FROM AUTHOR]

This article deals with the model predictive control (MPC) design problem for systems which are linearly dependent on a time-varying parameter. The main novelty is that, motivated by practical issues, the bounds on the rate of variation of the parameters are taken into account in the control design. Moreover, a Lyapunov function depending multiaffinely on the parameters computed at a set of instants of time and a parameter-dependent control gain are used to provide an upper bound to a quadratic performance index. The solution is obtained by means of a semidefinite programming algorithm. Examples illustrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC - in which an optimisation designs a tube for the system to follow rather than a trajectory - to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability analysis of quantised feedback control systems which contain the optimal dynamic quantisers recently proposed by the authors. First, it is shown that a sort of separation property of quantiser-controller design holds as far as the feedback system stability concerns. This allows us to design feedback controllers independently of the choice of quantisers. Then, based on this property, a necessary and sufficient condition is derived for the optimally quantised feedback system to be stable, which is described in terms of the poles/zeros of a linear feedback system to be quantised. Finally, we provide a class of suboptimal dynamic quantisers for which the resulting quantised control systems are guaranteed to be stable. [ABSTRACT FROM AUTHOR]

The paper addresses problems of numerical conditioning of the discrete-time H∞ control design based on J-lossless factorizations of the chain-scattering representation of a plant. It is demonstrated that for a sufficiently small sampling period forward-shift operator techniques may become ill-conditioned and numerical robustness and reliability of design procedures can be significantly improved by utilizing a so-called δ operator form of the source problem. State space models of all 3-domain controllers are given. The solutions are obtained by considering two coupled δ-domain algebraic Riccati equations that can be solved by applying a generalized eigenproblem formulation. Numerical conditioning of these solutions can effectively be evaluated by using a suitable relative condition number. An extended J-lossless factorization for generalized plants with zeros on the stability boundary circle is also given. A so-called zero compensator technique adapted to the δ-domain models is utilized to cancel such zeros and some attempt is made to simplify the resulting controller. Two numerical examples are given to illustrate the properties of the approach. The first example deals with a simple problem of mixed sensitivity H∞ design. The second example concerns a method for robust pole placement design for a plant with zero located on the boundary of the stability region. [ABSTRACT FROM AUTHOR]

The non-standard H ∞ control problem is the case where the direct feedthroughs from the input to the error and from the exogenous signal to the output are not necessarily of full rank. In this paper, this problem is reformulated based on the generalized chain-scattering representation (GCSR). The GCSR approach leads naturally to a generalization of the homographic transformation. The state-space realization for this generalized homographic transformation and a number of fundamental cascade structures of the H∞ control systems are further studied in a unified framework of GCSR. Certain sufficient conditions for the solvability of the non-standard H∞ control problem are therefore established via a (J, J ′)-lossless factorization of GCSR. These results present extensions to Kimura's results on the chain-scattering representation (CSR) approach to the H ∞ control in the standard case. [ABSTRACT FROM AUTHOR]

In this paper, a discontinuous dynamic state feedback that robustly stabilizes affine in control uncertain non-linear systems is proposed. The formulation is based on Hamilton–Jacobi–Isaacs partial differential equations with two boundary conditions. The resulting dynamic state feedback is then expressed in terms of the solution of the related PDEs. An interesting feature is that the internal state of the resulting dynamic state feedback may have discontinuous behaviour as a function of time. The proposed scheme is illustrated through the example of the stabilization of the angular velocities of a rigid body under two actuators. [ABSTRACT FROM AUTHOR]