This study investigates nonlinear reliable output tracking control issues. Both passive and active reliable control laws are proposed using Variable Structure Control technique. These reliable laws need not the solution of Hamilton-Jacobi (HJ) equation or inequality, which are essential for optimal approaches such as LQR and H reliable designs. As a matter of fact, this approach is able to relax the computational burden for solving the HJ equation. The proposed reliable designs are also applied to a bank-to-turn missile system to illustrate their benefits.

We consider a discrete event system controlled by a decentralized supervisor consisting of n local supervisors. Given a nonempty and closed language as the upper bound specification, we consider a problem to synthesize a reliable decentralized supervisor such that the closed-loop behavior is still legal under possible failures of any less than or equal to n-k (1 k n) local supervisors. We synthesize two such reliable decentralized supervisors. One is synthesized based on a suitably defined normal sublanguage. The other is the fully decentralized supervisor induced by a suitably defined centralized supervisor. We then show that the generated languages under the control actions of these two decentralized supervisors are incomparable.

In the design of nonlinear reliable controllers, one major issue is to solve for the solutions of the Hamilton-Jacobi inequality. In general, it is hard to obtain a closed form solutions due to the nonlinear nature of the inequality. In this paper, we seek for the existence conditions of quadratic type positive semidefinite solutions of Hamilton-Jacobi inequality. This is achieved by taking Taylor's series expansion of system dynamics and investigating the negative definiteness of the associated Hamilton up to fourth order. An algorithm is proposed to seek for possible solutions. The candidate of solution is firstly determined from the associated algebraic Riccati inequality. The solution is then obtained from the candidate which makes the truncated fourth order polynomial of the inequality to be locally negative definite. Existence conditions of the solution are explicitly attained for the cases of which system linearization possesses one uncontrollable zero eigenvalue and a pair of pure imaginary uncontrollable eigenvalues. An example is given to demonstrate the application to reliable control design problem.