Dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault

This paper investigates the problem of dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault. By using reduced-order observer method and switched Lyapunov function technique, a fault estimation algorithm is achieved for the discrete-time switched system with actuator fault. Then based on the obtained online fault estimation information, a switched dynamic output feedback fault tolerant controller is employed to compensate for the effect of faults by stabilizing the closed-loop systems. Finally, an example is proposed to illustrate the obtained results.     

Finite-time stabilization of state dependent impulsive dynamical linear systems

The problem of finite-time stabilizing control design for state-dependent impulsive dynamical linear systems (SD-IDLS) is tackled in this paper. Such systems are characterized by continuous-time, linear, possibly time-varying, dynamics coupled with discrete-time, linear, possibly time-varying, dynamics. The continuous-time part determines the system evolution in any time interval between two consecutive resetting events, while the discrete-time part governs its instantaneous state jump whenever the system trajectory intersects a resetting set, i.e. a region of the state space assumed to be time-independent. By making use of a quadratic control Lyapunov function, the finite-time stabilization of SD-IDLS through a static output feedback control design is specifically discussed in this paper. A sufficient and constructive result is provided based on the conical hulls of the resetting set subregions and on some cone copositivity properties of the chosen control Lyapunov function. Such a result is based on the solution of a feasibility problem that involves a set of coupled Difference/Differential Linear Matrix Inequalities (D/DLMI), which is shown to be less conservative and more numerically amenable with respect to other results available in the literature. An example illustrates the effectiveness of the proposed approach.     

Hybrid consensus for multi-agent systems with time-driven jumps

In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus behavior of the hybrid network is explicitly characterized. The hybrid multi-consensus is shown to be associated with a suitable partition that is almost equitable for both the jump and flow communication digraphs. In doing so, no assumption on the underlying digraphs is introduced. Finally, the coupling rules making the multi-consensus subspace attractive are established. Several simulation examples illustrate the theoretical results.     

Optimal Control of a Stochastic Hybrid System with Discounted Cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.     

Robust output feedback stabilization for two-dimensional continuous systems in roesser form

This paper considers the problem of robust stabilization via dynamic output feedbackcontrollers for uncertain two-dimensional continuous systems described by the Roesser's state space model. The parameter uncertainties are assumed to be norm-bounded appearing in all the matrices of the system model. A sufficient condition for the existence of dynamic output feedback controllers guaranteeing the asymptotic stability of the closed-loop system for all admissible uncertainties is proposed. A desired dynamic output feedback controller can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method.     

On the optimal design of the output transformation for discrete-time linear systems

The optimization of the output matrix for a discrete-time, single-output, linear stochastic system is approached from two different points of view. Firstly, we investigate the problem of minimizing the steady-state filter error variance with respect to a time-invariant output matrix subject to a norm constraint. Secondly, we propose a filter algorithm in which the output matrix at timek is chosen so as to maximize the difference at timek+1 between the variance of the prediction error and that of the a posteriori error. For this filter, boundedness of the covariance and asymptotic stability are investigated. Several numerical experiments are reported: they give information about the limiting behavior of the sequence of output matrices generated by the algorithm and the corresponding error covariance. They also enable us to make a comparison with the results obtained by solving the former problem.This work was supported by the Italian Ministry of Education (MPI 40%), Rome, Italy.     

State feedback and output feedback control of a class of nonlinear systems with delayed measurements

This paper is concerned with the problem of state feedback and output feedback control of a class of nonlinear systems with delayed measurements. This class of nonlinear systems is made up of continuous-time linear systems with nonlinear perturbations. The nonlinearity is assumed to satisfy a global Lipschitz condition and the time delay is assumed to be time-varying and have no restriction on its derivative. On the basis of the Lyapunov–Krasovskii approach, sufficient conditions for the existence of the state feedback controller and the output feedback controller are derived in terms of linear matrix inequalities. Methods of calculating the controller gain matrices are also presented. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Static output feedback and guaranteed cost control of a class of discrete-time nonlinear systems with partial state measurements

In this paper both the static output feedback issue and the observer-based control of a class of discrete-time nonlinear systems are considered. Thanks to a newly developed linearization lemma, it is shown that the solution of the discrete-time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint. An illustrative example is provided to show the usefulness of the proposed control designs.     

Impulsively-controlled systems and reverse dwell time: A linear programming approach

We present a receding horizon algorithm that converges to the exact solution in polynomial time for a class of optimal impulse control problems with uniformly distributed impulse instants and governed by so-called reverse dwell time conditions. The cost has two separate terms, one depending on time and the second monotonically decreasing on the state norm. The obtained results have both theoretical and practical relevance. From a theoretical perspective we prove certain geometrical properties of the discrete set of feasible solutions. From a practical standpoint, such properties reduce the computational burden and speed up the search for the optimum thus making the algorithm suitable for the on-line implementation in real-time problems. Our approach consists in approximating the optimal impulse control problem via a binary linear programming problem with a totally unimodular constraint matrix. Hence, solving the binary linear programming problem is equivalent to solving its linear relaxation. Then, given the feasible solution from the linear relaxation, we find the optimal solution via receding horizon and local search. Numerical illustrations of a queueing system are performed.     

Robust output feedback sliding mode control for uncertain discrete time systems

This paper proposes a robust output feedback controller for a class of uncertain discrete-time, multi-input multi-output, linear, systems. This method, which is based on the combination of discrete-time sliding mode control (DTSMC) and Kalman estimator, ensures the stability, robustness and an output tracking against the modeling uncertainties at large sampling periods. For this purpose, an appropriate structure is considered for sliding surface and the Lyapunov theory for the mismatched uncertain system is then used to design its parameter. This problem leads to solve a set of linear matrix inequalities. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show the effectiveness of the proposed method in the presence of parameter uncertainties and external disturbances at large sampling periods.     

State feedback controller design for singular positive Markovian jump systems with partly known transition rates

The paper deals with the problem of state feedback controller design for singular positive Markovian jump systems with partly known transition rates. First, by applying an appropriate linear co-positive type Lyapunov–Krasovskii function, stochastic stability of the underlying systems is discussed. Based on the results obtained, a state feedback controller is constructed such that the closed-loop singular Markovian jump system is regular, impulse-free, positive and stochastically stable. All the provided conditions are based on a reliable computational approach in linear programming. Finally, an example is given to demonstrate the validity of the main results.     

Numerical methods for controls for nonlinear stochastic systems with delays and jumps: applications to admission control

We consider numerical methods of the Markov chain approximation type for computing optimal controls and value functions for systems governed by nonlinear stochastic delay equations. Earlier work did not allow Poisson random measure driving processes or delays that are concentrated on points with positive probability. In addition, the Poisson measures can be controlled. Previous proofs are not adequate for the present case. The algorithms are developed and convergence proved as the approximating parameters go to their limits. One motivating example concerns admissions control to a network, where the file arrival process is governed by a Poisson process, and arrivals might be admitted or not, according to the control, which leads to a controlled Poisson process. Numerical data for such an example are presented. The original problem is recast in terms of a transportation equation, which allows the development of practical algorithms. For the problems of interest, alternative methods can entail prohibitive memory and computational requirements.     

Optimal output tracking control for nonlinear systems via successive approximation approach

This paper deals with the optimal output tracking control (OOTC) problem of a class of nonlinear systems whose reference input to be tracked is produced by a generalized linear exosystem. To solve the nonlinear OOTC problem, the nonlinear two-point boundary value (TPBV) problem derived from the necessary conditions of the OOTC problem is transformed into two decoupled iterative sequences of linear differential equations. The OOTC law obtained consists of accurate feedforward and feedback terms and a nonlinear compensation term. The former can be found by solving a Sylvester equation and a Riccati equation, and the latter can be approximated using a successive approximation approach (SAA). A reduced-order reference input observer is constructed to make the feedforward control law physically realizable. A simulation example is employed to illustrate the validity of the results.     

Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints

In this paper, smooth output feedback controllers are presented to stabilize a class of planar switched nonlinear systems with asymmetric output constraints (AOCs). A new common barrier Lyapunov function (CBLF) is developed to prevent the switched system from violating AOCs. Combining the adding a power integrator technique (APIT) and the CBLF, state feedback controllers are designed. Then, reduced-order nonlinear observers are constructed and smooth output feedback controllers are proposed to globally stabilize planar switched nonlinear systems under arbitrary switchings. Meanwhile, the system output meets the prescribed AOCs during operation. The method proposed in this paper is a unified tool because it works not only for switched nonlinear systems with asymmetric or symmetric output constrains but also for those without output constraints. Simulations are presented to verify the proposed method.     

A geometric approach for reachability and observability of linear switched impulsive systems

This paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices. First some new concepts with respect to the reachability and unobservability are introduced. Especially, span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces. Then the geometric characterization of the span reachable and unobservable sets is presented. Moreover, the relations between the span reachable set, unobservable set and the invariant subspaces of such systems are discussed. Finally, corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed.     

A novel approach on stabilization for linear systems with time-varying input delay

This paper presents new results on delay-dependent stability and stabilization for linear systems with interval time-varying delays. Some less conservative delay-dependent criteria for determining the stability of the time-delay systems are obtained in this paper. Based on the stability conditions, we propose a new state transformation technology to facilitate controller designing efficiently and computationally. The method is also applicable to the existing stability conditions reported by now, while the existing technologies may fail to derive computational control procedures from the stability conditions. Finally, some numerical examples well illustrate the effectiveness of the proposed method.     

Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays

This paper deals with output feedback guaranteed cost control problem for a general class of uncertain linear discrete delay systems, where the state and the observation output are subjected to interval time-varying delay. The proposed output feedback controller uses the observation measurement to exponentially stabilize the closed-loop system and guarantee an adequate level of system performance. By constructing a set of augmented Lyapunov–Krasovskii functionals, a delay-dependent condition for the robust output feedback guaranteed cost control is established in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the efficiency of the proposed method.