The paper presents an algorithm for the solution of the consensus problem of a {linear }multi-agent system composed of identical agents. The control of the agents is delayed, however, these delays are, in general, not equal in all agents. {The control algorithm design is based on the H∞-control, the results are formulated by means of linear matrix inequalities. The dimension of the resulting convex optimization problem is proportional to the dimension of one agent only but does not depend on the number of agents, hence this problem is computationally tractable. } It is shown that heterogeneity {of the delays in the control loop} can cause a steady error in the synchronization. Magnitude of this error is estimated. The results are illustrated by two examples.
Combat planes are designed in a structured relaxed static stability to meet maneuver requirements. These planes are unstable in the longitudinal axis and require continuous active control systems with elevator control. Therefore, failures in the elevator can have vital consequences for flight safety. In this work, the performance of classical control approach against asymmetric elevator failures is investigated and it is shown that this approach is insufficient in the case of such a failure. Then, a fault-tolerant control system is proposed to cope with these failures and it is shown that this controller can successfully deal with such failures. The F-16 aircraft is taken as an example case. A detailed nonlinear dynamic model of this aircraft is presented first. In the F-16 aircraft, the elevator surfaces are in two parts, right and left, and can move independently. Therefore, to obtain a more realistic and difficult failure scenario, it is assumed that the elevator is asymmetrically defective. Two types of failures commonly observed on the elevator surfaces (freezing and floating) are aerodynamically modeled and it is shown that the pitch-rate control augmentation systems in the conventional structure cannot cope with these elevator failures. In order to overcome this problem, a fault-tolerant control system is proposed. It is shown that this controller can successfully cope with the aforementioned failures without any degradation in flight safety.
This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example.
This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem of simultaneously minimizing a set of H∞ cost functions for a class of systems subject to bounded disturbances and/or parameter uncertainties. Numeric examples are reported to highlight the stabilizing action of the proposed control laws.
Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking problem. These solutions are based on proposed stabilizing gains solving a pole placement problem by output feedback. The proposed gains simplify the coprime factorizations of the plant and the controller, and allow assigning a decoupled characteristic polynomial. The 2DOF stabilizing control is based on the Parameterization of All Stabilizing Controllers (PASC) where the free parameter in the feedback part of the controller solves the mixed sensitivity robust control problem of attenuation of a Low-Frequency (LF) additive disturbance at the input of the plant and of a High-Frequency (HF) additive disturbance at the measurement, while the free parameter in the reference part of the controller assures that the controlled output tracks the reference at LF such as step or sinusoidal inputs. With the proposed expressions, the mixed sensitivity problem is solved without using weighting functions, so the controller does not increase its order; and the infinite norm of the mixed sensitivity criterion, as well as the assignment of poles, is determined by a set of control parameters.
This paper presents a procedure for constructing a stable decentralized output feedback controller for a class of uncertain systems in which the uncertainty is described by Integral Quadratic Constraints. The controller is constructed to solve a problem of robust H∞ control. The proposed procedure involves solving a set of algebraic Riccati equations of the H∞ control type which are dependent on a number of scaling parameters. By treating the off-diagonal elements of the controller transfer function matrix as uncertainties, a decentralized controller is obtained by taking the block-diagonal part of a non-decentralized stable output feedback controller which solves the robust H∞ control problem. This approach to decentralized controller design enables the controller to exploit the coupling between the subsystems of the plant.
The paper addresses the problem of the robust output feedback controller design with a guaranteed cost and parameter dependent Lyapunov function for linear continuous time polytopic systems. Two design methods based on improved robust stability conditions are proposed. Numerical examples are given to illustrate the effectiveness of the proposed methods. The obtained results are compared with other three design procedures.
This paper presents a new robust adaptive model predictive control for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound, as well as constraints on input states. An adaptive control is used in the new controller to estimate the system uncertainty. Also, to avoid the system disturbances, a H∞ method is employed to find the appropriate gain in Tube-MPC. Finally, a surge avoidance problem in centrifugal compressors is solved to show the efficiency and effectiveness of the proposed algorithm.