Robust and Adaptive Control with Output Feedback

Abstract

In this chapter, we shall introduce an observer-based adaptive output feedback tracking control design for multi-input multi-output controllable and observable dynamical systems with matched uncertainties. The emphasis is on adaptive controllers that operate based on available output feedback signals (measurements), as opposed to state feedback connections. We assume that the number of the system measured outputs (sensors) is no less than the number of the control inputs (actuators). If the number of inputs and outputs are the same, we would require that the system has relative degree one. Such an input–output property might be restrictive for a generic class of systems. We will be able to alleviate the relative-degree-one restriction by assuming that the system has more outputs than inputs and that the corresponding output-to-input matrix has full rank. It turns out that in this case, the system can be “squared-up” (i.e., augmented) using pseudo-control signals to yield relative-degree-one minimum-phase dynamics. Since the “squaring-up” problem is solvable for any controllable and observable triplet (A, B, C) (Misra P, Numerical algorithms for squaring-up non-square systems, Part II: General case. In: Proceedings of American Control Conference, San Francisco, CA, 1998), our proposed adaptive output feedback design is applicable to systems whose regulated output dynamics may be nonminimum phase or have a high relative degree. In its core, our adaptive output feedback design is based on asymptotic properties of linear quadratic Gaussian regulators with Loop Transfer Recovery (Doyle JC, Stein G, IEEE Trans. Autom. Control 26(1):4–16, 1981). In essence, our method combines robust and adaptive controllers in a unified output feedback framework. The design is formally justified, that is, we will be able to formulate sufficient conditions to guarantee closed-loop stability and uniform ultimate boundedness of the corresponding tracking error dynamics. At the end of this chapter, we will offer a flight control design case study to demonstrate key features and benefits of the method.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-1-4471-4396-3_15