Output Feedback Guaranteed Cost Control for Linear Uncertain System with Input Saturation

An LMI approach to guaranteed cost control of linear uncertain time-delay systems

This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed l2 to l∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H∞ performance criterion is also considered as well. Controllers with a guaranteed l2 to l∞ gain and a guaranteed H∞ performance (l2 to l2 gain) are a special family of mixed H2=H∞ controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed l2 to l∞ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed l2 to l∞ gain and >H∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.

This paper concerns the reliable guaranteed cost control problem of nonlinear systems with time-varying state delays and actuator failures for a given quadratic cost function. The problem is to design a delay-dependent reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop cost function value is not more than a specified upper bound. Based on the linear matrix inequality (LMI) approach, a sufficient condition for the existence of reliable guaranteed cost controllers is derived. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal reliable guaranteed cost controller which minimizes the upper bound of the closed-loop system cost. A numerical example is given to illustrate the proposed method.

This paper considers the output feedback guaranteed cost controller design problem for uncertain discrete-time systems. The uncertainty is assumed to be of linear fractional form, unstructured, and is allowed to be time-varying. It is proved that the existence of a guaranteed cost controller is equivalent to the feasibility of a certain linear matrix inequality (LMI), and that a full-order output feedback controller can be constructed in terms of the feasible solution to the LMI. Furthermore, a convex optimization problem is introduced for the selection of a suitable controller minimizing a specified cost bound.

This paper investigates the problem of delay-dependent output feedback guaranteed cost controller design for uncertain discrete-time switched systems with time-varying state delay. The uncertainties are assumed to have a structured linear fractional form. The objective is to design a switched dynamic output feedback controller guaranteeing the asymptotic stability of the resulting closed-loop system and minimizing a specified cost function. Based on a delay-dependent switched Lyapunov-Krasovskii functional (DDSLKF) combined with Finsler's Lemma, a novel delay-dependent robust performance analysis result is first proposed and in turn the output feedback controller synthesis is developed. It is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

The linear Markov jump model that is usually used in the analysis and design phases is an approximation of a real nonlinear system with Markov jumps in the neighborhood of the operating point. For many reasons well known in the control community, the systems parameters and the operating point change with time and therefore, the fixed linear Markov jump model is not adequate to guarantee robustness of system performance. Besides this, the system can be affected by exogenous disturbances, which will make the degradation worse. To overcome this surprise, the control engineer should take care of these uncertainties and exogenous disturbances during the analysis and design phases to guarantee the required stability and other system performance, despite the presence of uncertainties in the system. The results presented so far for the class of linear systems with Markov jumps and time delay are not adequate to guarantee the robustness of the desired performance. The robust H∞ control problem was developed to maintain robustness of stability and performance when it known algorithms lack robustness, that is, the system parameters have uncertainties. This chapter deals with the robust H∞ control and the guaranteed cost control problems for jump linear systems with norm-bounded uncertainties and time delay. The rest of the chapter is organized as follows.we deal with the robust H∞ control problem. considers he guaranteed cost control problem. we cover the output feedback guaranteed cost control problem.

This paper deals with the guaranteed cost control problem for a class of uncertain linear discrete-time switched systems with time-delay under arbitrary switching laws. The purpose is to design a state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. A sufficient condition on the existence of guaranteed cost controllers is derived based on Lyapunov theory together with linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMIs constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

The problem of robust guaranteed cost control for a class of uncertain stochastic systems with Markov jump parameters subject to actuator saturation is discussed. The concept of domain of attraction is used to analyze the stochastic stability and a sufficient condition which guarantees the intersection of ellipsoid invariant set under different modes in the domain of attraction is presented. The solvability condition of robust guaranteed cost controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller such that the closed-loop system is stochastically stable and the cost function value is minimized. A numerical example is given to verify the effectiveness of this method.

The paper concerns stability analysis of hybrid systems. The main contribution is the proposed approach of discrete-time modeling of continuous-time hybrid systems. Stability analysis and robustness properties are derived from linear Lyapunov theory in discrete time. The method is especially suited for time-switched systems but can also incorporate more complex switch structures. It is also shown how periodic switch sequences fit into the analysis. The resulting problem formulations are given as linear matrix inequalities (LMIs). As an alternative to the S-procedure it is shown how to reduce conservativeness with a reduction of the LMIs state dimension when the switch regions are hyper planes. An example shows that the number of LMIs and LMI variables are reduced compared to a continuous-time approach.

Robust guaranteed cost control for uncertain linear differential systems of neutral type

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

Relaxed linear matrix inequalities (LMIs) conditions for fuzzy observer-based controller design are proposed based on a kind of improved T-S fuzzy model structure. The improved structure included the original T-S fuzzy model and enough large bandwidth pre- and post-filters. By this structure fuzzy observer-based controller design can be transformed into LMIs optimization problem. Compared with earlier results, it includes the less number of LMIs that equals the number of fuzzy rules plus one positive definition constraint of Lyapunov function. Therefore, it provides us with less conservative results for fuzzy observer-based controller design. Finally, a numerical example is demonstrated to show the efficiency of proposed method.

Fixed-Order H∞ Control Design via a Partially Augmented Lagrangian Method