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In this paper, the problem of designing static output feedback (SOF) H 2 negative imaginary controller has been studied. Because the constraints brought by negative imaginary (NI) property and H 2 performance are a set of bilinear matrix inequalities (BMIs), designing an SOF NI controller with H 2 performance is a non-trivial problem. To overcome the difficulty of solving BMIs, a linearisation-based method is proposed. First, a necessary and sufficient condition is established, where the constraints of NI property and H 2 performance are reformulated as similar forms. Second, inspired by the semidefinite programming, the derived condition is converted to the difference between two convex functions. Then a linearised iterative algorithm with initialisation process is provided to compute the desired SOF H 2 NI controller. Finally, two numerical examples are presented to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the security issue of the data replay attacks on control systems with the LQG controller. The attacker tries to store measurements and replay them in further times. The main novelty in this paper is stated as proposing a different attack detection criterion under the existence of a packet-dropout feature in the network by using the Kullback-Leibler divergence method to cover more general problems and with higher-order dynamics. Formulations and numerical simulations prove the effectiveness of the newly proposed attack detection procedure. Unlike previous approaches that the trade-off between attack detection delay or LQG the performance was significant, in this approach it is proved that the difference in this trade-off is not considered in early moments when the attack happens since the attack detection rate is rapid and thus, the attacks can be stopped with defense strategies in the first moments with the proposed attack detection criterion. [ABSTRACT FROM AUTHOR]

This paper deals with the control performance assessment of distributed networked control systems in the presence of communication delays. The best achievable steady-state performance of distributed networked control systems in the framework of distributed linear quadratic Gaussian (LQG) control is presented where communication delays serve as the most fundamental performance limitation. In the proposed distributed LQG control design, distributed controllers and distributed observers are designed simultaneously without using separation principle. And the non-applicability of separation principle is investigated and demonstrated in distributed networked control with communication delays. In order to handle time-varying communication delays, we propose to use lower and upper bounds to characterize the range of the best achievable control performance with respect to the range of the communication delays. The obtained results can be used to evaluate the potential performance improvement of an existing distributed networked control system. The proposed approach is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

This paper addresses the design of static output feedback controller for linear discrete-time systems. New sufficient criteria are derived for designing H ∞ and H 2 controllers. The corresponding design criteria are presented in the form of Linear Matrix Inequalities (LMIs). The development involves certain relaxations of the LMI variables through appropriate use of bounding inequalities leading to less conservative LMI design criteria. The proposed method is compared with existing ones through numerical examples to illustrate the effectiveness of the design method. [ABSTRACT FROM AUTHOR]

We revisit the issue of quadratic gain-scheduled and robust state-feedback control with a focus on linear matrix inequalities widely used in the literature. It has been established that for continuous-time linear parameter-varying systems which depend affinely on the scheduling parameter, gain-scheduled stabilisability implies robust stabilisability. In other words, as far as stabilisation is concerned, using a more complex gain-scheduled controller is not advantageous. The proof of such equivalence is non constructive and, although very general, limited to stabilisability. One contribution of the present paper is to establish constructive proofs in the quadratic case that can be extended to performance optimisation in terms of quadratic H 2 and H ∞ norms. One issue investigated in detail is the strategy of using pre-filters to handle parameter-variation in the input matrix. Our results show that said technique, which has been popular since the 1980s, is rarely productive in the sense that solvability of quadratic gain-scheduled control design problems for the original system augmented with an arbitrary pre-filter implies existence of a lower-dimensional quadratic robust controller for the original system, which we construct explicitly via projections. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) andH∞optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as ‘coherent feedback controller’. A lower bound of the LQG control is proved. Then two different methods, rank-constrained linear matrix inequality method and genetic algorithm are for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier) demonstrate the effectiveness of these two proposed algorithms. [ABSTRACT FROM PUBLISHER]

This paper focuses on the optimal control design for a system of coupled parabolic–hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear–quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances. [ABSTRACT FROM AUTHOR]

This paper presents a composite control strategy integrating adaptive sliding-mode control and the linear quadratic regulator (LQR) technology for a wheeled inverted pendulum (WIP) vehicle system. The system can be partitioned into an actuated rotational subsystem and an underactuated longitudinal subsystem based on the different control input in the mathematical model. In particular, the instability analysis of zero dynamic for the underactuated longitudinal subsystem is investigated in detail using the feedback linearisation technology. Then, an adaptive sliding-mode control is designed for the trajectory tracking, where an adaptive algorithm is developed to handle with the parameter uncertainties. In addition, the LQR technique is employed to guarantee zero dynamics stability so as to achieve simultaneously the vehicle body stabilisation at the upright position. Simulation results show the good performance and strong robustness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper is concerned with theH2/H∞control problem for stochastic linear systems with delay in state, control and external disturbance-dependent noise. A necessary and sufficient condition for the existence of a unique solution to the control problem is derived. The resulting solution is characterised by a kind of complex generalised forward–backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the equivalent feedback solution via a new type of Riccati equations. To explain the theoretical results, we apply them to a population control problem. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of optimal and robustH2control for discrete-time periodic systems with Markov jump parameters and multiplicative noise. To analyse the system performance in the presence of exogenous random disturbance, anH2norm is firstly established on the basis of Gramian matrices. Further, under the condition of exact observability, a necessary and sufficient condition is presented for the solvability ofH2optimal control problem by means of a generalised Riccati equation. When the transition probabilities of jump parameter are incompletely measurable, anH2-guaranteed cost norm is exploited and the robustH2controller is designed through a linear matrix inequality (LMI) optimisation approach. An example of a networked control system is supplied to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This article presents a robustness bound (RB) of receding horizon finite memory control (RHFMC) (Kwon, W.H., and Han, S. (2004), ‘Receding Horizon Finite Memory Controls of Output Feedback Controls for State Space Systems’, IEEE Transactions on Automatic Control, 49, 1905–1915) for continuous-time state-space systems with norm-bounded uncertainties. The proposed RB is easily obtained by solving a convex problem in terms of a linear matrix inequality. We show through a numerical example that the RHFMC can guarantee the robust stabilisation for a larger class of uncertain systems than linear quadratic Gaussian controls when some poles of closed-loop systems are close to an imaginary axis in the complex plane. [ABSTRACT FROM AUTHOR]

In this work, the boundary control of a distributed parameter system modelled by linear parabolic partial differential equations (PDEs) with spatially varying coefficients is studied. An infinite-dimensional state space setting is considered and an exact transformation of the boundary actuation is realised to obtain an evolutionary model. The evolutionary model which incorporates the spatially varying coefficients of the underlying set of the PDEs is used for subsequent linear quadratic regulator synthesis. The formulated linear quadratic-state feedback controller is applied to a nonlinear model of the reactor and its performance is studied. [ABSTRACT FROM AUTHOR]

This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed. [ABSTRACT FROM AUTHOR]

A novel approach to the design of a less conservative model predictive control is proposed, using mixed H2/H∞ design method for time-invariant discrete-time linear systems. The controller has the form of a state-feedback, satisfies input and state constraints and is constructed from the solution of a set of feasibility linear matrix inequalities. The control law takes into account the disturbances naturally and the input constraint is less conservative in the sense that the full control is used. Numerical examples comparing the proposed algorithm with some existing techniques are provided to demonstrate the applicability and the advantage of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Given a plant transfer matrix as a fraction of two polynomial matrices, we present a doubly coprime factorisation identity over the proper stable rational matrices of the plant transfer matrix, and apply it to compute a controller transfer matrix in H2 optimal control of discrete-time systems. If there are no uncontrollable modes of the plant transfer matrix, the controller is given by a fraction of two polynomial matrices, where the order of the denominator is less than or equal to the McMillan degree of the plant. [ABSTRACT FROM AUTHOR]

Real-time control of a physical system necessitates controllers that are low order. In this article, we compare two balanced truncation methods as a means of designing low-order controllers for a nonlinear cable-mass system. The first is the standard technique of balanced truncation. The second, linear quadratic Gaussian (LQG) balanced truncation, can be thought of as balancing based on the controller, and states that are important from the perspective of control and filter design are retained. The control design applied to each reduced-order model is the central controller. We provide an overview of the central controller and devote attention to the design of this controller in the presence of balancing. Also described in this article is a method for reducing computational time in solving algebraic Riccati equations for the design of low-order LQG balanced controllers. [ABSTRACT FROM AUTHOR]

This article addresses the H2 norm accumulation problem of linearly coupled dynamical networks. An interesting outer-coupling relationship is constructed, under which the H2 norm of the newly constructed network with column-input and row-output matrices increases exponentially fast in terms of the node number N: it increases generally much faster than 2N when N is large while the H2 norm of each node is 1. However, the H2 norm of the network with a diffusive coupling is equal to γ2 N, i.e. increasing only linearly, when the network is stable, where γ2 is the H2 norm of a single node. And the H2 norm of the network with antisymmetrical coupling also increases, but rather slowly, with respect to the node number N. Other networks with block-diagonal-input and block-diagonal-output matrices behave similarly. It demonstrates that the changes of H2 norms in different networks are very complicated, despite the fact that the network structures are linear. Finally, the influence of the H2 norm of the locally linearised network on the output of a network with Lur'e node dynamics is discussed, demonstrating a significant effect of the H2 norm on the network output synchronisation behaviours. [ABSTRACT FROM AUTHOR]

A minimax linear quadratic (LQ) output-feedback controller is introduced which minimises the maximal value of the performance index over all initial states belonging to some set separated out a priori. If the set is an ellipsoid or a polygon, such controllers are synthesised in terms of linear matrix inequalities (LMIs). In particular case when a size of this set tends to zero tightening to a point, the minimax LQ controller approaches the optimal LQ output-feedback controller for the given initial state, while in another extreme case when this size tends to infinity, we have the worst-case LQ output-feedback controller. Numerical results for an inverted pendulum are presented. [ABSTRACT FROM AUTHOR]

This article introduces a new approach to H2 robust filtering design for continuous and discrete-time LTI systems subjected to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load. [ABSTRACT FROM AUTHOR]

The H2 control problem is formulated with exogenous inputs having unstable shape-deterministic components. Such inputs are called persistent. Some issues in connection with past solutions of the H2 control problem in this case are carefully described and addressed. In particular, it is established that two- and three-degree-of freedom (2DOF and 3DOF) systems with persistent inputs cannot be treated within the framework of the standard configuration. In addition, past treatments of persistent inputs within the framework of the generalised 2DOF configuration focused on solutions which yielded stable error transforms without explicitly requiring the same for controller outputs. In this article, a more general configuration is treated and physical considerations are invoked to justify imposition of the requirement that both the regulated variable z(s) and the controller output u(s) be stable. A persistent input model for which there exists a stabilising controller that makes both z(s) and u(s) stable is called acceptable and the necessary and sufficient condition for such acceptability is determined. Also considered is a persistent input model for which there exists a stabilising controller that makes the controller output, the measured output and the regulated variable stable. Such a model is called strictly acceptable and the necessary and sufficient condition for strict acceptability is given. The subset of all stabilising controllers associated with an acceptable persistent input model is parameterised and this parameterisation is used to formulate an H2 optimisation problem with persistent inputs which can then be solved using standard procedures. [ABSTRACT FROM AUTHOR]

The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying catalytic reactor. First, the dynamical properties of the linearised model are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related matrix Riccati partial differential equation. Finally, the designed controller is applied to the non-linear reactor system and tested numerically. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of infinite-horizon discrete-time linear quadratic N-person games, in which one of the players lacks complete information about the game. With the assumptions of a perfect state information pattern and steady state feedback strategies, we convert the original game problem into a multivariable adaptive control problem by making use of the concept of fictitious play and the scheme of adaptive control. For the proposed adjustment procedure, we prove that each element of the estimates converges to its corresponding true value under the condition of persistent excitation. We also carry out a sensitivity analysis of performance indices with respect to the embedded unknowns by using multiple models. [ABSTRACT FROM AUTHOR]

Classical linear time-invariant system simulation methods are based on a transfer function, impulse response, or input/state/output representation. We present a method for computing the response of a system to a given input and initial conditions directly from a trajectory of the system, without explicitly identifying the system from the data. Similar to the classical approach for simulation, the classical approach for control is model-based: first a model representation is derived from given data of the plant and then a control law is synthesised using the model and the control specifications. We present an approach for computing a linear quadratic tracking control signal that circumvents the identification step. The results are derived assuming exact data and the simulated response or control input is constructed off-line. [ABSTRACT FROM AUTHOR]

In this article, upper bounds on the worst-case H2 performance index relative to structured, feedback perturbations are considered which are based on the minimisation of dual Lagrangean functionals over linearly-parametrised, finite-dimensional classes of dynamic multipliers. It is shown that the minimisation problems in question can be recast as optimisation problems with linear cost functional and Linear matrix inequality (LMI) constraints. An iterative scheme is suggested to generate linearly-parametrised classes of multipliers of increasing dynamic order so that progressively tighter upper bounds can be obtained, as illustrated by two simple numerical examples. Finally, with a view to synthesis procedures based on 'D-K iterations' relative to multipliers and controllers, it is shown that the minimisation of the upper-bounds corresponding to given multipliers with respect to linearly-parametrised classes of Youla parameters can also be cast as linear-cost/LMI-constraint problems. [ABSTRACT FROM AUTHOR]

An overlapping decentralized control scheme is presented and applied to automatic generation control (AGC) for multi-area power systems. Based on the inclusion principle, the system is first decomposed in the expanded space as a group of pair-wise subsystems (areas). Then, the decentralized controllers designed, by standard linear quadratic (LQ) control laws are implemented in each pair-wise subsystem. Finally, the overlapping decentralized controller is obtained by coordinating and contracting the pair-wise decentralized controllers from the expanded space to the original space, preserving the inclusion conditions. When applied to AGC of a four-area power system, the proposed methodology not only guarantees AGC qualities, but also increases the system reliability with respect to a wide variety of structured perturbations. Simulation results illustrate the effectiveness of the presented approach both in the general case of information structure constraints and in the cases when some pairs of subsystems are disconnected by unpredicted faults. [ABSTRACT FROM AUTHOR]

In this paper, the generation of time signals in a network node based on the weighting of phases from two master signals is studied. A discussion about the stability of such a system is conducted with techniques of multi-variable robust control. Designing compensators by using multi-variable linear quadratic gaussian (LQG) and loop transfer recovery (LTR) robust control techniques seems to improve the response of the whole clock generation process, even in the presence of parasitic poles. [ABSTRACT FROM AUTHOR]

The homogeneous charge compression ignition (HCCI) combustion engine principle lacks direct ignition timing control, instead the auto-ignition depends on the operating condition. Since auto-ignition of a homogeneous mixture is very sensitive to operating conditions, fast combustion phasing control is necessary for reliable operation. For this paper, a six-cylinder heavy-duty HCCI engine was controlled on a cycle-to-cycle basis in real time. Sensors, actuators and control structures for control of the HCCI combustion were compared. Among several actuators for HCCI engine control suggested, two actuators were compared—i.e., dual-fuel actuation and variable valve actuation (VVA). As for control principles, model predictive control (MPC) has several desirable features and today MPC can be applied to relatively fast systems, such as VVA and dual-fuel actuation. For sensor feedback control of the HCCI engine, cylinder pressure and ion current—i.e., the electronic conductive properties in the reaction zone—were compared. Combustion phasing control based on ion current was compared to control based on cylinder pressure. For the purpose of control synthesis requiring dynamic models, system identification provided models of the HCCI combustion, the models being validated by stochastic model validation. With such models providing a basis for model-based control, MPC control results were compared to PID and LQG control results. While satisfying the constraints on cylinder pressure, both control of the combustion phasing and control of load torque was achieved with simultaneous minimization of the fuel consumption and emissions. [ABSTRACT FROM AUTHOR]

This paper presents a computationally tractable moving horizon control scheme, where the to be on-line solved minimax problem is relaxed to a minimization problem by Lagrange duality. This helps the avoidance of infeasibility and reduction of conservation caused by the ellipsoid evaluation of time-domain constraints. Disturbance attenuation with performance adaptation is achieved by on-line monitoring of the dissipation level and accumulating the ‘energy reserve’ from performance relaxations that are necessary for the satisfaction of time-domain constraints. Simulation and comparison results confirm the advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents results concerning LQ control of arbitrary descriptor systems and a numerical algorithm for achieving it. The algorithm consists of two steps. The first step is, using the Silverman algorithm (orthogonal version), transformation of the problem of LQ control of descriptor system, into a problem of LQ control of a strictly proper system (with singular or non-singular new matrix S 22 ). If new S 22 is singular, we perform the second step, i.e. solving the LQ singular control problem using again the Silverman algorithm. Regarding the existing results on the LQ singular control problem, we have new results: a counter example that this problem may not have a stable solution, most general solvability conditions (with or without stability), and a new numerical algorithm based on using orthogonal matrices. When stabilizability conditions are satisfied, the algorithm places simultaneously stable poles in the closed-loop system. We show that the traditional Riccati equation associated to this problem has not a solution (although the problem has), and introduce a generalization of Riccati equation, together with a method for its solving, as well as a generalization of spectral factorization of Popov function. Examples that cannot be solved by the existing methods are presented. [ABSTRACT FROM AUTHOR]

This communication is concerned with the problem of stabilization, via output static feedback, of linear time-invariant finite-dimensional systems. A new output static stabilization concept is introduced: output static stabilization in the relaxed sense. This conservative stabilization concept is the result of imposing an additional condition to a set of necessary and sufficient conditions for output static stabilization. This paper is devoted to exhaustively study the introduced new stabilization concept: (I) It is shown that for a particular class of plants, the stabilization problem in the above sense can be cast as a convex programming problem. (II) A full characterization of the class of plants that are stabilizable in the above new sense is presented. Some of the important consequences of that study are as follows: (1) The identification of a class of plants stabilizable, via output static feedback, for which stabilizing feedback matrices can be (almost) expressed in analytic closed form. (2) It is shown that the introduced new conservative stabilization concept is much more significant that it appears; the general problem of output static stabilization can be transformed into the stabilization problem in this new conservative sense. (3) A relationship between output static stabilizability and the LQR problem is proved. (4) A novel generalization of the famous Lyapunov's theorem is presented. Convex necessary and sufficient conditions, for joint stabilization (of multiple plants) in the above sense and, for decentralized stabilization in the above sense, are also presented. Numerical examples illustrate some of the results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust H 2 and H ∞ control of discrete linear time-invariant (LTI) systems with polytopic uncertainties via dynamic output feedback. The problem has been known to be difficult when a parameter dependent Lyapunov function is to be applied for a less conservative design due to non-convexity. Our approach is based on a novel bounding technique that converts the non-convex optimization into a convex one together with a line search, which is simple but may be conservative. To further reduce the design conservatism, an algorithm based on the sequentially linear programming method (SLPMM) is proposed. A numerical example is given which demonstrates the feasibility of the proposed design methods. [ABSTRACT FROM AUTHOR]

This paper considers a control system for a crane that reduces pendulation of suspended loads in offshore lifting operations. The modelling of the ship crane is studied and an anti-pendulation arm is designed and proposed. Two different types of models are derived, one based on torque and one kinematic. For the torque model, Lyapunov analysis and non-linear control design is applied on the vertical plane. Linear control design techniques for the linearized kinematic model are applied in both vertical and horizontal planes. These techniques are based on linear quadratic Gaussian (LQG) and generalized predictive control (GPC). The advantage for the linear control designs is the explicit use of the vessel dynamics and sea wave disturbances in the control design that considerably improves the controlled pendulation of the crane. Design issues, simulation results and comparison studies are considered. [ABSTRACT FROM AUTHOR]

An algorithm for checking feasibility of the robust H∞-control problem for systems with time-varying norm bounded uncertainty is suggested. This algorithm is an iterative procedure on each step of which an optimization problem for a linear function under convex constraints determined by LMIs is solved. The effectiveness of the proposed algorithm is demonstrated on the numerical example of a parametrically disturbed pendulum. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of model reduction for linear discrete-time state-delay systems. For a given stable system, our attention is focused on the construction of reduced-order models, which guarantee the corresponding error system to be asymptotically stable and have a prescribed error performance. Both delay-independent and dependent approaches are developed, with sufficient conditions obtained for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved in standard numerical software. In addition, the development of reduced-order models with special structures, such as delay-free models and zeroth-order models, is also addressed. The approximation methods presented in this paper can be further extended to cope with systems with uncertain parameters. Two numerical examples have been provided to show the effectiveness of the proposed theories. [ABSTRACT FROM AUTHOR]

Using the Hamiltonian function method, this paper investigates the adaptive H ∞ excitation control of multimachine power systems with disturbances and parameter perturbations. A key step in applying the Hamiltonian function method to the multimachine system is to express the system as a dissipative Hamiltonian system, i.e. to complete dissipative Hamiltonian realization (DHR). By using pre-feedback technique, this paper expresses the multimachine power system as a dissipative Hamiltonian system. Then, the stability analysis of the achieved dissipative Hamiltonian system is proceeded. Finally, based on the achieved DHR form, the adaptive H ∞ excitation control of the multimachine power system is investigated and a decentralized simple excitation control strategy is obtained. Simulations on a six-machine system show that the adaptive H ∞ excitation control strategy proposed in the paper is more effective than some other control schemes. [ABSTRACT FROM AUTHOR]

The optimal LQG tracking problem is studied both for available and for unavailable state and reference, assuming that the last variable is the addition of a known deterministic component and of a random noise component. In both cases the optimal solution exists, is unique, and the optimal control is a suitable affine function of the current state and reference variable (when they are available) or of the corresponding optimal estimates (when they are not available). The minimum cost function is expressed in closed form. [ABSTRACT FROM AUTHOR]

For linear-quadratic dynamic games in which norm-bounded time-varying uncertainty enters in all matrices of the system equation without assuming the matching conditions, the notions of robust minimax and maximin strategies are introduced. It is shown how to construct two auxiliary dynamic games with completely known equations in such a way that a minimax strategy for one of them and a maximin strategy for the other turn out to be the robust minimax and maximin strategies, respectively, for the original dynamic game. By assuming 'control' as the first player and 'disturbance' as the second player, we show that the robust minimax strategy in the appropriate dynamic game provides the uncertain system with a robust H infinity suboptimal control, which guarantees quadratic stability of the unforced uncertain system. The results presented in this paper generalize those obtained in previous works. [ABSTRACT FROM AUTHOR]

This paper describes the synthesis of non-fragile or resilient regulators for linear systems. A general framework for fragility is described using state-space methodologies, and the LQ/H[sub 2] static state-feedback problem is examined in detail. We discuss the multiplicative structured uncertainties case, and propose remedies of the fragility problem using an optimization programming framework via matrix inequalities. A special case that leads to a convex optimization framework via linear matrix inequalities (LMIs) will be considered. The benchmark problem is taken as an example to show how special controller gain variations can affect the performance of the closed-loop system. [ABSTRACT FROM AUTHOR]

This paper is an extension of our previous work regarding realization of LQ optimal systems using output feedback in which we showed that the solutions existed when the plant satisfied certain conditions. In this paper, we remove the restrictions set forth in our previous work and present a design which is suitable for any LQ optimal system. This design involves feedback consisting of scalar output, even when a multivariable system is the subject of the design. Moreover, both the discrete-time and the continuous-time formulations of the proposed design are formulated. The present method also combines plant model estimation and control design into a single procedure by using a technique which achieves an output feedback LQ design directly from plant input and output data, thereby eliminating the need for explicit identification of a parametric plant model. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithmic solution to the infinite horizon linear quadratic optimal control problem for a discrete-time SISO plant subject to bound constraints on a scalar variable. The solution to the corresponding quadratic programming problem is based on the active set method and on dynamic programming. It is shown that the optimal solution can be updated after inclusion or removal of an active constraint by a simple procedure requiring in the order of kn operations, n being the system order and k the time at which the constraint is included or removed. [ABSTRACT FROM AUTHOR]

This paper establishes necessary and sufficient conditions for existence, uniqueness and global optimality of the Linear Quadratic Coupled Delay Compensator (LQCDC) which is designed to circumvent the detrimental effects of randomly varying delays from sensor to controller and from controller to actuator as well as the time skew caused by missynchronization of sensor and controller sampling instants. These conditions are derived on the basis of the concepts of stabilizability, detectability and compensatability in the mean square sense. In the absence of random delays from sensor to controller and from controller to actuator, it has been shown that LQCDC problems reduce to the classical Linear Quadratic Gaussian (LQG). [ABSTRACT FROM AUTHOR]

This paper presents a family of observers which has as particular cases the 'unknown input observers' and the 'linear quadratic/H2/Hinfinity optimal observers'. A smooth transition between these particular extreme cases through the general case is provided, corresponding to a transition of the disturbance patterns from entirely 'singular' to entirely 'regular' ones. Both 'hard' (arbitrary) and 'soft' (Gaussian or l2 signals) disturbances are allowed. The methodology presented here, although developed for discrete time systems, may be extended to the continuous time case. [ABSTRACT FROM AUTHOR]

A class of linear quadratic regulators of the system with time-delay in the states is constructed by a memoryless feedback, and its robustness is evaluated. First, a static non-linear perturbation is inserted in the input channel, and a robust stability condition is derived. As its special case, it is shown that the regulator has infinite gain margin and at least 50% gain reduction tolerance. Next, a dynamic linear perturbation is inserted in the same point, and an alternative stability condition is derived. It assures that the regulator has at least 60o phase margin. These results coincide with those of the finite dimensional LQ regulator. [ABSTRACT FROM AUTHOR]

Solves the problem of minimizing the time taken by a two-dimensional diffusion process to hit the boundary of a certain termination region. Consideration of a mathematical expectation for a different uncontrolled process; Extension of the results about LQG homing problems.

Considers the robust H[sup 2] control problem of finding a controller satisfying the prescribed H[sup 2] performance level against all possible uncertainty under the constraint of robust stability. Derivation of a sufficient condition for the robust H[sup 2] performance in terms of a linear matrix inequality; Design method of a descriptor variable feedback controller.

Addresses the Linear Quadratic Regulator Problem with a positivity constraint on the admissible control set. Necessary and sufficient conditions for optimality; Pontryagin's maximum principle and dynamic programming; Smoothness of the optimal control and the value function.