Optimal output feedback control of discrete linear, singularly perturbed, stochastic systems

This paper studies the composite anti-disturbance static output feedback control problem of networked nonlinear Markov jump systems with general transition probabilities subject to multiple disturbances and deception attacks. The transition probabilities cover the known, uncertain with known bounds, and unknown cases. The unmatched disturbance and deception attacks are attenuated by the static output controller, while the matched disturbance is observed and compensated by the disturbance observer. Then, a composite anti-disturbance static output controller, including a linear part and a nonlinear part, is constructed to satisfy the stochastic H∞ stability. By using the Finsler lemma, sufficient conditions formed as symmetric linear matrix inequalities are derived to design the gains of disturbance observer and the output feedback controller. Finally, some simulations are given to illustrate the feasibility of the developed strategy.

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of high-precision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.

We investigate the design of a static output feedback control for switching discrete time systems. Looking at the problem of stability analysis, we give two conditions allowing to check the existence of a particular class of Lyapunov functions. Although one can recover the first condition as a particular case from the second one, it is proved that the two conditions are equivalent for stability analysis. Then we show that when one is faced with a static output feedback control problem, the second condition leads to a sufficient solution to build a stabilizing static output feedback controller which is less conservative than the solution based on the first condition.

Improved stability criterion and output feedback control for discrete time-delay systems

This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0<α<1 subject to input saturation with convex polytopic uncertainties, by a kind of [Formula: see text]–proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ([Formula: see text]) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism.

In this paper, a new type of control, called a receding horizon finite memory control (RHFMC) or a model predictive finite memory control, is proposed as an optimal output feedback control for stochastic state-space systems. Constraints such as linearity, finite memory structure, and unbiasedness from the optimal state feedback control are required in advance, and in addition, the performance criterion of quadratic cost is required. Constraints for the input and the state are not assumed in this paper. The RHFMC is obtained directly by minimizing the performance criterion for stochastic state-space systems with the previous constraints. It is shown that the RHFMC can be separated into a receding horizon control and a finite-impulse response filter. The stability of the RHFMC is investigated. The validity of the proposed RHFMC is illustrated by a numerical example.

A linear parameter varying approach for designing a constant output feedback controller for a linear time-invariant retarded system with stochastic multiplicative Wiener-type noise, that achieves a minimum bound on the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level is introduced. The stochastic uncertainties appear in the dynamic matrices, which correspond to the delayed and non-delayed states of the system, and in the measurement matrix of the system. The solution of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output-feedback control problem is solved, for the stationary case, via the input-output approach where the system is replaced by a non-retarded system that contain, instead, deterministic norm-bounded uncertainties. In this problem, a cost function is defined which is the expected value of the standard H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance cost with respect to the stochastic parameters. We extend the results achieved for the nominal case, to the uncertain case where the system matrices lie within a given polytop.

This paper investigates the static output feedback control problem for discrete-time positive linear systems subject to state delay, actuator constraints, and resource limitations in communication. To address these challenges simultaneously, an event-triggered control framework is developed. A novel event-triggering condition is proposed, based on a component-wise comparison where the triggering error is checked against state-dependent bounds. Sufficient conditions for ensuring positivity, exponential stability, and satisfaction of input constraints are derived. Crucially, these design conditions are formulated as a set of solvable linear programming problems, making the approach computationally tractable. Furthermore, conditions are established to demonstrate a provably reduced control update frequency compared to traditional time-triggered control, quantifying the resource-saving benefits of the proposed approach. Two numerical examples, including one based on a population dynamics model, illustrate the effectiveness of the proposed approach.

This paper considers the problems of designing multivariable proportional-integral-derivative (PID) controllers for discrete-time systems with D-stability and/or performance constraints. First, the PID control problem is cast into a static output feedback (SOF) control problem, and linear matrix inequality (LMI) conditions are presented. Then, a cone complementarity linearisation (CCL) method is used to solve the SOF-stabilisation problem, and a coordinate transformation matrix (CTM) optimisation approach is extended to solve the optimal SOF control problem. Finally, a numerical example is provided to show the effectiveness and advantage of the CTM optimisation approach, and application to the anti-sway and positioning control of an overhead crane demonstrates the validity of the approach.

Output feedback [formula omitted] finite-time control of switched positive delayed systems with MDADT

This paper is focused on the static output feedback (SOF) control problem for a class of switched nonlinear systems with actuator faults. By means of the Takagi-Sugeno fuzzy model, the switched nonlinear plant is described by a family of switched fuzzy systems. Considering transmission failures may occur between controller and actuator, a reliable SOF controller against actuator faults is designed. Sufficient conditions are developed to guarantee the existence of the reliable SOF controller. Furthermore, an iterative algorithm is designed to determine the controller gains, which avoids the conservatism brought by the traditional singular value decomposition method. To validate the effectiveness of the proposed approach, a numerical example is exploited and simulation results are also presented.

ABSTRACTThis paper investigates the static output feedback control problem for linear systems. The sensor and actuator may simultaneously suffer the total/partial loss of effectiveness. An adaptive fault-tolerant control scheme is developed by combination of linear matrix inequality method and adaptive mechanism. By estimating the inverses of failure factors online, the adverse effects of sensor and actuator failure can be compensated for. Finally, simulation results on the ‘Raptor-90’ helicopter verify the effectiveness of the proposed approaches.

Distributed Optimal Output Feedback Control of Heterogeneous Multi-agent Systems under a Directed Graph

This paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete-time domain. The approach followed in this paper looks at the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function. The first one is classical while the second is new and uses a slack variable, which makes it useful for design problems. These two conditions are proved to be equivalent for stability analysis. Investigating the static output feedback control problem, we show that the second condition is, in this case, less conservative. The reduction of the conservatism is illustrated by a numerical evaluation.

The standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty. In the case where the latter polytope is large, the design may become very conservative. We present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem. Assuming that there is online information on which of the regions the parameters of the system move to, a recently developed method for H∞ design of switched system with dwell time is applied. A Lyapunov Function (LF) in a quadratic form, which is non-increasing at the switching instants, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the L2 -gain of the switched system. The obtained results are used to solve the corresponding robust H∞ state-feedback and static output-feedback control problems.