Douglas A. Lawrence

Gain scheduling dynamic linear controllers for a nonlinear plant

For a general type of nonlinear tracking problem, we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points. A necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented. Using this condition, the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed, and ad hoc approaches to scheduling can be analyzed.

On a stability theorem for nonlinear systems with slowly varying inputs

Recently, M. Kelemen (IEEE Trans. Automat. Contr., vol.AC-31, 766-768, Aug. 1986) presented a stability result that deals with the response of a nonlinear system to slowly varying input signals. In this work a proof is given, under a weaker hypothesis on the input signal, by constructing a Lyapunov function that is standard in the control literature. This proof may be more accessible than the other approaches. For completeness, brief proofs of some intermediate results that are regarded as well known are included. A simple example is given to show that this approach can yield explicit bounds in certain situations of interest. >

Brief paper: Reachability and observability of linear impulsive systems

Linear impulsive systems constitute a class of hybrid systems in which the state propagates according to linear continuous-time dynamics except for a countable set of times at which the state can change instantaneously. While in general these impulsive effects can be time-driven and/or event-driven, here we focus our attention on the time-driven case. For this class of systems, we address the fundamental concepts of reachability and observability. In particular, we present a geometric characterization of the reachable and unobservable sets in terms of invariant subspaces and provide algorithms for their construction.

Input-output pseudolinearization for nonlinear systems

An input-output pseudolinearized system has the property that its family of linearizations about constant operating points has input-output behavior that is independent of the operating point. We develop a necessary and sufficient condition for existence of a state feedback and state coordinate change that transforms a given system into a pseudo-normal form that is input-output pseudolinearized. These ideas are applied to obtain new approaches to approximate tracking and approximate inversion of nonlinear systems. >

Brief paper: State feedback stabilization of linear impulsive systems

We address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily-spaced impulse times and possibly singular state transition matrices. Specifically, we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed-loop system. The approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well-known results for time-varying linear systems for both continuous and discrete-time cases.

Missile autopilot design using a gain scheduling technique

A recently developed framework for gain scheduled control system synthesis is applied to a missile autopilot design problem. In contrast to previous approaches, low order linear autopilots designed at discrete operating points using classical control techniques are gain scheduled. Also, mach number, modeled as a measured, time-varying exogenous signal, is viewed as a disturbance to be rejected in the linear design phase, leading to improved steady-state tracking performance.<<ETX>>

State estimation for linear impulsive systems

In this paper, we treat the fundamental problem of state estimation for a class of linear impulsive systems with time-driven impulsive effects. We show that a strong observability property enables an impulsive observer to be constructed that yields uniformly exponentially stable estimation error dynamics. This approach accommodates impulsive systems with arbitrarily-spaced impulse times and singular state transition matrices in a manner reminiscent of well-known results for time-varying discrete-time linear systems. As an example, an observer is constructed for an impulsive system that produces general cubic spline signals

Output regulation for linear systems with sampled measurements

Shows that if output regulation with internal stability is achievable via continuous-time error feedback then the same is true using sampled error feedback, discrete-time compensation, and a generalized hold device that generates the continuous-time control signal. In this scheme, the memoryless generalized hold together with the dynamic discrete-time compensator act as a continuous-time internal model of the exosystem. The approach involves casting the hybrid sampled-data system as a continuous-time system with periodically occurring jumps. Basic geometric concepts of invariant and controlled invariant subspaces are developed for linear systems with jumps to facilitate the analysis and the construction of compensators that solve the problem.

A general approach to input-output pseudolinearization for nonlinear systems

A nonlinear system is said to be input-output pseudolinearized if its family of linearizations about constant operating points has input-output behavior that is independent of the particular operating point. The problem of constructing static state feedback laws that achieve input-output pseudolinearization for a general class of nonlinear systems is considered. A generalization of the well-known structure algorithm to the case of parameterized families of linear systems plays an important role.

Brief Analysis and design of gain scheduled sampled-data control systems

The existence of gain scheduled sampled-data controllers that meet an important linearization requirement about a family of equilibria is investigated.