Robust partially mode delay dependent ℋ ∞ control of discrete-time networked control systems

This article proposes a methodology for designing a partially mode delay dependent ?_∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controller are modelled by a finite state Markov chain where the transition probability matrix is partially known. Stability criteria are obtained based on Lyapunov–Krasovskii functional and a novel methodology for designing a partially mode delay dependent state feedback controller has been proposed. The controller is obtained by solving linear matrix inequality optimisation problems using cone complimentarity linearisation algorithm. A numerical example is provided to illustrate the effectiveness of the proposed controller.     

Robust direct model reference adaptive control using KP = LDU factorization for multivariable plants

Motivated by the idea of high frequency gain matrix K_P ?=?LDU factorization, the purpose of this paper is to study the problem of robust direct model reference adaptive control for more general multivariable plants with unmodeled dynamics and disturbances. For multivariable plants, by reproving some properties similar to those in robust adaptive control theory for SISO plants and redefining the normalizing signal, the relationship between all the signals in the closed-loop plant and the normalizing signal can be established, and the stability and robustness of the closed-loop plant are analyzed rigorously from a qualitative point of view.     

Towards a less conservative model predictive control based on mixed ℋ2/ℋ ∞ control approach

A novel approach to the design of a less conservative model predictive control is proposed, using mixed ?₂/?_∞ 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.     

Robust H2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with normbounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities ( LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared tothe existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

Robust H_2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

Robust ℋ2 filtering for LTI systems with linear fractional representation

This article introduces a new approach to ?₂ 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.     

Adaptive dynamic surface control for a class of output-feedback nonlinear systems with guaranteed ℒ∞ tracking performance

In this article, an output-feedback adaptive dynamic surface control (DSC) is proposed for a class of nonlinear systems. It is proved that, by using the new scheme, the explosion of the complexity problem in a traditional backstepping design can be eliminated, the semi-global stability of a closed-loop system can be guaranteed and, in particular, by choosing the design parameters and initialising the filters and the update law properly, we show that the ?_∞ performance of the system-tracking error can be achieved without over-parametrisation. Another advantage of the proposed scheme compared with those traditional backstepping control and current adaptive DSC schemes, whose adaptive control law is obtained through a series of steps recursively, is that the adaptive law is needed only at the first design step, and therefore significantly reduces the design procedure.     

Robust H 2 and H ∞ control of discrete-time systems with polytopic uncertainties via dynamic output feedback

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.     

Robust H ∞ model predictive control for uncertain systems using relaxation matrices

In this paper, a robust H _∞ model predictive control (MPC) technique is proposed for time-varying uncertain discrete-time systems in the presence of input constraints and disturbances. We formulate a minimization problem of the upper bound of finite horizon cost function subject to the terminal inequality for an induced l ₂-norm bound. In order to improve system performance, we propose an LMI condition for the terminal inequality by using relaxation matrices. The LMI condition guarantees induced l ₂-norm bounds of the system despite system uncertainty and disturbance. A numerical example shows the effectiveness of the proposed method.     

On general ℋ2 control: from frequency to time domain

This article presents a general formula for discrete-time ?₂ control. It works with the regular and singular case of ?₂ control, i.e. in the case of possibly non-left-invertible matrices G ₁₂ and non-right-invertible matrices G ₂₁, with possible unit circle invariant zeros. In the generic case, it can be simplified and adapted to work with the plant transfer matrix directly, without invoking the matrices of the parameterisation of stabilising controllers. A further result of this article is the presented necessary and sufficient conditions for state-space ?₂ control, under only stabilisability and detectability assumptions. If the conditions are satisfied, an observer-based ?₂ controller is constructed. The corresponding numerical algorithm consists of solving two discrete-time algebraic Riccati systems (DARSs) and two eigen-problems.     

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

This paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H_∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.     

Robust H ∞ consensus control concerning second-order multi-agent systems with time-varying delays on dynamic topologies

Robust H _∞ consensus control for second-order multi-agent systems is addressed. Considering the delayed directed networks with disturbances and uncertainty parameters on dynamic topologies, the consensus protocols are proposed and analysed. By constructing the common Lyapunov–Krasovkii functional, applying the Lyapunov–Krasovkii theory and integral inequality approach, the sufficient condition of consensus protocol convergence is derived, guaranteeing robust H _∞ consensus for given second-order multi-agent systems. Finally, numerical examples are provided to demonstrate the effectiveness of the main results.     

Robust tracking control for uncertain Euler–Lagrange systems via dynamic event-triggered and self-triggered ADP

This article investigates the robust tracking control problem for a class of Euler–Lagrange systems in presence of parameter uncertainties and external disturbances. Through system transformation and theoretical analysis, an adaptive dynamic programming (ADP) algorithm with two adaptive neural networks (NNs) and a suitable triggering mechanism is proposed to attain the robust stability of the closed-loop system. A single critic NN is leveraged to implement the approximate optimal controller design. Particularly, an NN-based feedforward compensation is developed to cope with the uncertainties with unknown bounds. Two different triggering mechanisms are respectively constructed to reduce the budget of sampling, communication and computation, namely the dynamic event-triggering mechanism (DETM) and the self-triggering mechanism (STM). The DETM is utilized to decide the update of remote controller and critic NN weight, which can yield a larger inter-event interval than the static event-triggering mechanism. Also, the Zeno-free behavior is guaranteed. Moreover, it is a novel attempt to introduce the STM into ADP design, which relaxes the demand of dedicated hardware online monitoring the event-triggering condition. Then it is demonstrated that all signals in the closed-loop system are uniformly ultimately bounded (UUB) via Lyapunov-based stability analysis. Finally, a simulation example of 2-link robotic system is implemented to verify the feasibility and effectiveness of the proposed algorithm.     

H ∞ output-feedback LPV control for systems with input saturation

This paper investigates the problem of designing a dynamic H _∞ output-feedback controller under an L _∞ performance representing componentwise input constraints. In order to derive a less conservative stabilization condition therein, this paper introduces a Lyapunov function-based polytopic control law and proposes a method capable of applying the information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as convex polytope. Through this paper, the resultant H _∞/L _∞ problem is efficiently solved based on the set invariance condition formulated in terms of linear matrix inequalities (LMIs).     

Robust and stochastic model predictive control: Are we going in the right direction?

Motivated by requirements in the process industries, the largest user of model predictive control, we re-examine some features of recent research on this topic. We suggest that some proposals are too complex and computationally demanding for application in this area and make some tentative proposals for research on robust and stochastic model predictive control to aid applicability     

Robust adaptive output stabilization using dynamic normalizing signal

For a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered in this paper. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct an exp-ISpS Lyapunov function for the unmodeled dynamics, prove that the unmodeled dynamics is exp-ISpS, and then obtain a dynamic normalizing signal to counteract the dynamic disturbances. By the backstepping technique, an adaptive controller is given, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded, and the output can be regulated to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.     

H ∞ control for non-linear stochastic systems: the output-feedback case

The H _∞ output-feedback control problem for non-linear stochastic systems is considered. A solution for a large class of non-linear stochastic systems is introduced (including non-linear diffusion systems as a subclass). This solution is based on a bounded real lemma for non-linear stochastic systems that was previously established via a stochastic dissipativity concept. The theory yields sufficient conditions for the closed-loop system to possess a prescribed L ₂-gain bound in terms of two Hamilton Jacobi inequalities: one that is associated with the state feedback part of the problem is n-dimensional (where n is the underlying system's state dimension) and the other inequality that stems from the estimation part is 2n-dimensional. Both stationary and non–stationary systems are considered. Stability of the closed-loop system is established, both in the mean-square and the in-probability senses. As the solution to the Hamilton Jacobi inequalities may, in general, lead to a non–realisable state estimator, a modification of the associated 2n-dimensional Hamilton Jacobi inequality is made in order to circumvent this realisation problem, while preserving the system's L ₂-gain bound. For time-invariant systems, the problem of robust output-feedback is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear state-dependent matrix inequalities.     

Robust synchronisation tracking control of networked Euler–Lagrange systems using reference trajectory estimation based on virtual double-integrators

This paper considers the problem of distributed synchronisation tracking control of multiple Euler–Lagrange systems on a directed graph which contains a spanning tree with the leader node being the root. To design the high performance distributed controllers, a virtual double-integrator is introduced in each agent and is controlled by a virtual distributed linear high-gain synchronisation tracking controller, so that the position and velocity of each agent track those of the reference trajectory with arbitrarily short transient time and small ultimate tracking error. Then taking the double-integrator's position and velocity as the estimates of those of the reference trajectory, in each generalised coordinate of each Euler–Lagrange agent, a local controller with a disturbance observer and a sliding mode control term is designed, to suppress the mutual interactions among the agents and the modelling uncertainties. The boundedness of the overall signals and the synchronisation tracking control performance are analysed, and the conditions for guaranteed control performance are clarified. Simulation examples are provided to demonstrate the performance of the distributed controllers.     

Robust adaptive control for interval time-delay systems

1 Introduction The problem of time-delay is commonly encountered in various engineering systems, such as electric, pneumatic and hydraulic networks, long transmission lines, etc., and it is also a great source of systems instability and poor perfor- mance. During the last decades, we have seen an increasing interest for the control of this class of systems and many results have reported in the literature [1～5]. On the other hand, it has been recognized that nonlinear uncertainties are unavoid…     

Delay-dependent robust ℋ ∞ control for uncertain stochastic time-delay system

This article deals with the problem of robust stabilisation and ?_∞ control for a class of uncertain stochastic time-delay system. The parametric uncertainties are real time-varying and norm bounded. The aim is to design a memoryless state-feedback control law such that the closed-loop system are robustly stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such control law are presented based on the linear matrix inequalities approach. Numerical examples are given to illustrate the effectiveness of the developed techniques.