A framework of robust fault estimation observer design for continuous‐time/discrete‐time systems

A design framework of the observer‐based robust fault estimation for continuous‐time/discrete‐time systems is presented in this paper. Firstly, a multiconstrained fault estimation observer under the H_∞ performance specification with the regional pole constraint is proposed to achieve robust fault estimation. Then, the existence conditions for both continuous‐time/discrete‐time systems are derived explicitly. Furthermore, by introducing slack variables, improved results on the multiconstrained fault estimation observer design are obtained such that different Lyapunov functions can be separately designed for each constraint. Finally, simulation results of a vertical takeoff and landing aircraft are presented to illustrate our contributions. Copyright © 2012 John Wiley & Sons, Ltd.     

Polynomial matrix solution of H2 optimal control problem for state‐space systems

A polynomial matrix solution to the H₂ output feedback optimal control problems is obtained for systems represented in state‐equation form. The proof does not invoke the separation principle but is obtained in the z‐domain. The cost function includes weighted states, which allows the so‐called standard system model problem to be solved. This encompasses the class of inferential control problems. The results also enable the two‐degree‐of‐freedom optimal control solution properties to be explored. Copyright © 2002 John Wiley & Sons, Ltd.     

Distributed controller design and performance optimization for discrete‐time linear systems

This article addresses the problem of distributed controller design for linear discrete‐time systems. The problem is posed using the classical framework of state feedback gain optimization over an infinite‐horizon quadratic cost, with an additional sparsity constraint on the gain matrix to model the distributed nature of the controller. An equivalent formulation is derived that consists in the optimization of the steady‐state solution of a matrix difference equation, and two algorithms for distributed gain computation are proposed based on it. The first method consists in a step‐by‐step optimization of said difference matrix equation, and allows for fast computation of stabilizing state feedback gains. The second algorithm optimizes the same matrix equation over a finite time window to approximate asymptotic behavior and thus minimize the infinite‐horizon quadratic cost. To assess the performance of the proposed solutions, simulation results are presented for the problem of distributed control of a quadruple‐tank process, as well as a version of that problem scaled up to 40 interconnected tanks.     

Reduced‐order observer‐based fault estimation and fault‐tolerant control for a class of discrete Lipschitz nonlinear systems

This paper addresses an issue on reduced‐order observer‐based robust fault estimation and fault‐tolerant control for a class of uncertain nonlinear discrete‐time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced‐order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO‐based output feedback fault‐tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Implementation lessons and pitfalls for real‐time optimal control with stochastic systems

Modern computational power and efficient direct collocation techniques are decreasing the solution time required for the optimal control problem, making real‐time optimal control (RTOC) feasible for modern systems. Current trends in the literature indicate that many authors are applying RTOC with a recursive open‐loop structure, relying on a high recursion rate for implicit state feedback to counter disturbances and other unmodeled effects without explicit closed‐loop control. The limitations of using rapid, instantaneous optimal solutions are demonstrated analytically and through application to a surface‐to‐air missile avoidance control system. Two methods are proposed for control structure implementation when using RTOC to take advantage of error integration through either classical feedback or disturbance estimation. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

Robust stabilization of hybrid uncertain stochastic systems by discrete‐time feedback control

This paper aims to stabilize hybrid stochastic differential equations with norm‐bounded uncertainties by feedback controls based on the discrete‐time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of a stochastic differential equations, and the controlled system will be robustly exponentially stable in mean square. Our stabilization criteria are in terms of linear matrix inequalities whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

Inverse optimal control for discrete‐time nonlinear systems via passivation

This paper presents an inverse optimal control approach for stabilization and trajectory tracking of discrete‐time nonlinear systems, avoiding to solve the associated Hamilton–Jacobi–Bellman equation, and minimizing a meaningful cost functional. The proposed controller is based on a discrete‐time control Lyapunov function and passivity theory; its applicability is illustrated via simulations for an unstable nonlinear system and a planar robot. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based actuator fault estimation and proportional derivative fault tolerant control for continuous‐time singular systems

This paper focuses on designing fault estimation (FE) and fault tolerant control (FTC) schemes for continuous‐time singular systems affected by actuator fault. A novel observer called the extended proportional integral observer (PIO) is designed so that the estimations of system state and actuator fault can be obtained simultaneously. In contrast with the traditional PIO, better estimation performance can be obtained by using the designed observer. Furthermore, with the obtained FE information, a novel proportional derivative–type FTC scheme is given by means of the separation property and the free‐weighting matrix technique, which ensures that the closed‐loop system is normal and stable. All the feasible conditions are formulated in linear matrix inequality (LMI) frameworks. Finally, two examples are simulated to prove the superiority and practicability of the presented scheme.     

Finite‐time convergence results in robust model predictive control

Robust asymptotic stability (asymptotic attractivity and ?‐δ stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite‐time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite‐time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set‐based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite‐time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.     

Improved reachable set estimation of discrete‐time systems with time‐varying delay

This paper is concerned with the problem of reachable set estimation of discrete‐time systems with time‐varying delay and bounded disturbance. By applying the improved reciprocally convex combination approach to bound the forward difference of the double summation and triple summation, respectively, a less conservative reachable set estimation condition is developed in matrix inequalities. Based on the criterion, a less conservative stability criterion is obtained as a by‐product. Numerical examples are presented to validate the effectiveness of the obtained results.     

Unified approach for open‐loop optimal control

We develop a unified approach for the necessary conditions for optimization of open‐loop control systems, starting from the basic principles of calculus of variations. The unified approach results are simultaneously applicable to both shift (q)‐operator‐based, discrete‐time systems and the derivative (d/dt)‐operator‐based, continuous‐time systems. It is shown that the optimal condition results that are now obtained separately for continuous‐time and discrete‐time systems can be easily obtained from the unified approach. An illustrative example is given. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust satisfactory fault‐tolerant control of continuous‐time interval systems with time‐varying state and input delays

With the performance constraints on exponential stability, H_∞ norm of disturbance attenuation and upper bound of quadratic cost performance, the satisfactory and passive fault‐tolerant control problem is investigated for a class of interval systems with time‐varying input and state delays in the case of possible actuator faults. The bounded‐varying dynamics of actuator faults is described by interval matrix, which is more general and can be dealt with by the interval system theory. The delay‐dependent satisfactory fault‐tolerant controller design is developed based on multi‐objective optimization strategy. The results are derived in the forms of linear matrix inequalities, which is convenient to be solved in practice. Simulative example is presented to illustrate the effectiveness and necessity of the proposed fault‐tolerant control strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal integral sliding mode control for a class of uncertain discrete‐time systems

This paper considers the problem of sliding mode control for a class of uncertain discrete‐time systems. Firstly, an optimal control law for the nominal system is derived to satisfy linear quadratic performance index. And then, an optimal integral sliding surface is designed to ensure the robustness for sliding dynamics. By combining with the discrete reaching law, the existence condition of the sliding mode is proved, and the bandwidth of the quasi‐sliding mode is given. It is shown that the present method utilizes a lower control gain to attain stronger robustness and eliminate the chattering. Finally, illustrative simulation results are provided. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal stabilizing controllers for linear discrete‐time stochastic systems

The relationship between the spectral radius and the decay rate for discrete stochastic systems is investigated. Several equivalent conditions are obtained, which guarantee a specified decay rate of the closed‐loop systems. Based on the relationship, this paper provides a design method for state feedback controllers, which ensure that the closed‐loop systems converge as fast as possible. Finally, a numerical example is used to illustrate the developed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Reliable control for interval time‐varying delay systems subjected to actuator saturation and stochastic failure

This paper is devoted to the problem of reliable control for interval time‐varying delay systems subjected to actuator saturation and stochastic failure. A new practical actuator fault model is proposed by assuming that the actuator fault obeys a certain probabilistic distribution. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. Delay distribution and fault distribution‐dependent estimations of the domain of attraction are obtained by using the LMI techniques and an optimization method, such that the mean‐square stability of the systems can be guaranteed for given H_∞ performance index γ. Two illustrative examples are exploited to show the effectiveness of the proposed design procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

Singular linear quadratic optimal control for singular stochastic discrete‐time systems

The finite time horizon singular linear quadratic (LQ) optimal control problem is investigated for singular stochastic discrete‐time systems. The problem is transformed into positive LQ one for standard stochastic systems via two equivalent transformations. It is proved that the singular LQ optimal control problem is solvable under two reasonable rank conditions. Via dynamic programming principle, the desired optimal controller is presented in terms of matrix iterative form. One simulation is provided to show the effectiveness of the proposed approaches. Copyright © 2012 John Wiley & Sons, Ltd.     

A 2D‐based approach to guaranteed cost repetitive control for uncertain discrete‐time systems

This paper presents a two‐dimensional (2 D)‐based approach to the problem of guaranteed cost repetitive control for uncertain discrete‐time systems. The objective is to design a control law such that the closed‐loop repetitive control system is robustly stable and a certain bound of performance criteria is guaranteed for all admissible uncertainties. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2 D system. Then, sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal guaranteed cost control law by minimizing the upper bound of the cost function. The proposed approach is applicable not only to SISO systems, but also to MIMO systems. Two numerical examples are provided to demonstrate the effectiveness of the proposed controller design procedures. Copyright © 2010 John Wiley & Sons, Ltd.     

Full delayed state feedback pole assignment of discrete‐time time‐delay systems

This paper studies the problem of pole assignment of discrete‐time time delay system with delayed state feedback. The problem is solved in this paper by requiring that the maximal delay in the feedback equals the maximal delay of the open‐loop system. A necessary and sufficient condition guaranteeing the existence of a solution is presented. By using the augmentation technique, the pole assignment problem is then transformed to the problem of solving a linear matrix equation such that certain conditions are satisfied. To solve the linear equation problem, when the desired closed‐loop eigenvalues are not prescribed, a parametric approach using real arithmetic is presented by using polynomial matrices associated with the system matrices. When the desired closed‐loop eigenvalues are prescribed, singular value decomposition can be adopted to solve the linear matrix equation. Both approaches can provide full degree of freedom, which can be further utilized to accomplish some other design objects. The robust pole assignment problem is considered to demonstrate the advantages of the method. Numerical examples are employed to illustrate the effectiveness of the proposed approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Estimation and synthesis of reachable set for discrete‐time periodic systems

This paper is concerned with the problems of reachable set estimation and synthesis for discrete‐time periodic systems under bounded peak disturbances. For the reachable set estimation problem, the lifting approach and the pseudo‐periodic Lyapunov function approach are utilized to determine the bounding ellipsoids for the reachable set. By using the lifting approach, the periodic system is transformed into several time‐invariant systems; then, the bounding ellipsoids are determined through the transformed time‐invariant systems. By applying the pseudo‐periodic Lyapunov function approach, the bounding ellipsoids are determined through the original periodic system directly. Genetic algorithm is adopted in the pseudo‐periodic Lyapunov function approach to search for the optimal value of the decision variables. Moreover, based on the reachable set estimation results, state‐feedback controllers are designed for manipulating the reachable set. Finally, numerical examples are presented to verify the effectiveness of the theoretical findings. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control for discrete‐time systems with actuator saturation

In this study, we use generalized policy iteration approximate dynamic programming (ADP) algorithm to design an optimal controller for a class of discrete‐time systems with actuator saturation. A integral function is proposed to manage the saturation nonlinearity in actuators and then the generalized policy iteration ADP algorithm is developed to deal with the optimal control problem. Compared with other algorithm, the developed ADP algorithm includes 2 iteration procedures. In the present control scheme, 2 neural networks are introduced to approximate the control law and performance index function. Furthermore, numerical simulations illustrate the convergence and feasibility of the developed method.