Supervisory control of switching control systems

In this thesis, we show that the problem of designing a switching policy for an adaptive switching control system can be formulated as a problem of Supervisory Control of a Discrete-Event System (DES). Two important problems in switching control are then addressed using the DES formulation and the theory of supervisory control under partial observation. First we examine whether for a given set of controllers, a switching policy satisfying a given set of constraints (on the transitions among controllers) exists. If so, then we design a minimally restrictive switching policy. Next, we introduce an iterative algorithm for finding a minimal set of controllers for which a switching policy satisfying the switching constraints exists. In our study we show that in the supervisory control problem considered in this thesis, limitation on event observation is the factor that essentially restricts supervisory control. In other words, once observation limitations are respected, limitation on control will be automatically satisfied. We use the above result to simplify our iterative algorithm for finding minimal controller set

Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach

On observer design for a class of impulsive switched systems

In this thesis, the problem of state observation for a class of impulsive switched systems is addressed. Corresponding to each subsystem, an identity Luenberger observer is employed and a switching observer is constructed accordingly. The asymptotic stability property of the proposed switching observer is discussed and LMI-based algorithms are given which provide necessary conditions for the asymptotic stability of the switching observer for the switching signals with an average dwell time greater than a specific value. Since switched systems without impulse are a special case of impulsive switched systems, all the results in this work can be applied to design observers for switched systems without impulse. The design of finite time switching observers for a class of linear switched systems is another problem addressed in this work. The finite convergence time property of the proposed switching observer is discussed and the exponential stability of the observation error is investigated. An LMI-based algorithm is given which provides conditions for the exponential stability of the switching observer. Finally, the idea of finite time observers for linear continuous time systems is extended to linear time invariant discrete time systems. The main motivation for this extension is that unlike the famous dead-beat observers designed for discrete time systems, the proposed observer in this work need not place all the eigen-values at the origin, which leads to a much more flexible design compared to the existing techniques

Stability analysis and controller design for switched time-delay systems

In this thesis, the stability analysis and control synthesis for uncertain switched time-delay systems are investigated. It is known that a wide variety of real-world systems are subject to uncertainty and also time-delay in their dynamics. These characteristics, if not taken into consideration in analysis and synthesis, can lead to important problems such as performance degradation or instability in a control system. On the other hand, the switching phenomenon often appears in numerous applications, where abrupt change is inevitable in the system model. Switching behavior in this type of systems can be triggered either by time, or by the state of the system. A theoretical framework to study various features of switched systems in the presence of uncertainty and time-delay (both neutral and retarded) would be of particular interest in important applications such as network control systems, power systems and communication networks. To address the problem of robust stability for the class of uncertain switched systems with unknown time-varying delay discussed above, sufficient conditions in the form of linear matrix inequalities (LMI) are derived. An adaptive switching control algorithm is then proposed for the stabilization of uncertain discrete time-delay systems subject to disturbance. It is assumed that the discrete time-delay system is highly uncertain, such that a single fixed controller cannot stabilize it effectively. Sufficient conditions are provided subsequently for the stability of switched time-delay systems with polytopic-type uncertainties. Moreover, an adaptive control scheme is provided to stabilize the uncertain neutral time-delay systems when the upper bounds on the system uncertainties are not available a priori . Simulations are provided throughout the thesis to support the theoretical result

Aircraft loss-of-control prevention and recovery: a hybrid control strategy

The Complexity of modern commercial and military aircrafts has necessitated better protection and recovery systems. With the tremendous advances in computer technology, control theory and better mathematical models, a number of issues (Prevention, Recon guration, Recovery, Operation near critical points, ... etc) moderately addressed in the past have regained interest in the aeronautical industry.Flight envelope is essential in all ying aerospace vehicles. Typically, ying the vehicle means remaining within the ight envelope at all times. Operation outside the normal ight regime is usually subject to failure of components (Actuators, Engines, Deection Surfaces) , pilots's mistakes, maneuverability near critical points and environmental conditions(crosswinds...) and in general characterized as Loss-Of-Control (LOC) because the aircraft no longer responds to pilot's inputs as expected.For the purpose of this work,(LOC) in aircraft is de ned as the departure from the safe set (controlled flight) recognized as the maximum controllable (reachable) set in the initial ight envelope. The LOC can be reached either through failure, unintended maneuvers, evolution near irregular points and disturbances. A coordinated strategy is investigated and designed to ensure that the aircraft can maneuver safely in their constraint domain and can also recover from abnormal regime. The procedure involves the computation of the largest controllable (reachable) set (Safe set) contained in the initial prescribed envelope. The problem is posed as a reachability problem using Hamilton-Jacobi Partial Di erential Equation(HJ - PDE) where a cost function is set to be minimized along trajectory departing from the given set. Prevention is then obtained by computing the controller which would allow the flight vehicle to remain in the maximum controlled set in a multi-objective set up. Then the recovery procedure is illustrated with a two - point boundary value problem. Once illustrate, a set of control strategies is designed for recovery purpose ranging from nonlinear smooth regulators with Hamilton Jacobi-Bellman (HJB) formulation to the switching controllers with High Order Sliding Mode Controllers (HOSMC). A coordinated strategy known as a high level supervisor is then implemented using the multi-models concept where models operate in specified safe regions of the state space.Ph.D., Mechanical Engineering and Mechanics -- Drexel University, 201