Robust output feedback control of incompletely observable nonlinear systems without input dynamic extension

M. Maggiore, K. Passino
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)  
We introduce a new output feedback controller for general MIMO nonlinear systems which are only observable on regions of the state and input spaces. Unlike previous approaches, we do not add integrators at the input side of the system, and thus avoid the need to design a stabilizing control law for a higher order system. Robustness with respect to a class of time-varying disturbances is guaranteed, and the performance of any state feedback controller designed to achieve closed-loop stability
more » ... h respect to a set (e.g., a robust controller) is recovered. 1 3. This estimate is employed in the state feedback control law and control saturation is used to guarantee its global boundedness. Unfortunately, this approach cannot be used when the system is not uniformly completely observable (UCO), i.e., when the system is observable only on regions of the state and input spaces. For example, the Moore-Greitzer model describing the dynamics of stall and surge in jet engine compressors is not observable when there is no mass flow through the engine, and there currently seems to be no solution for this engine output feedback control problem based on a separation principle. In [7, 8] we introduced a new methodology for solving this class of more general output feedback control problems. This technique replaces points 2 and 3 above with the following: 2'. A nonlinear state observer that depends on the integrators' states is designed to directly estimate the system states. 3'. The state estimate is modified via a projection method so that it lies within an observable region and guarantees global boundedness when it is employed in the closed-loop. In [7, 8] we proved that by using this technique a separation principle similar to the one formulated in [6] is achieved and, in [9, 10], this methodology was applied to derive a solution to the stall and surge control problem described above. In this work we extend the theory developed in [7, 8] to deal with MIMO nonlinear systems affected by time-varying disturbances, and for which a state feedback control law can be designed that robustly stabilizes the system (hence, a suitable compact set N is made attractive and positively invariant by the state feedback control law; notice the similarity with the work in [11]). A major difference between this work and other approaches, including our previous results, is the substitution of point 1 above with the following: 1'. A high-gain (or, alternatively, sliding mode) observer is employed for the estimation of the control input derivatives (or, equivalently, the states of the integrators used in the input dynamic extension in point 1). Essentially, rather than adding a chain of integrators at the input side of the system, we use an observer to estimate the control input derivatives (hence, our observer has higher order but the overall controller order is the same). This modification results in a simplification of the control design problem in that the original state feedback controller can be directly employed by the output feedback controller (i.e., we eliminate the need to design a control law for the higher-order "extended system" in point 1 above). We prove that, in the presence of disturbances, this approach guarantees uniform ultimate boundedness (UUB) of the closed-loop system trajectories with respect to N (in complete analogy with the result of Theorem 4 in [11] , but here we do not investigate conditions needed on the disturbance so that asymptotic stability is recovered). When no disturbance affects the system, it is shown that a design that is based on a sliding mode observer recovers the asymptotic stability of the closed-loop system with respect to N , while the high-gain observer achieves UUB. In summary, via the results in [7, 8] and here we replace the procedure given by 1,2 and 3 that is studied in [2, 6] by the procedure given by 1', 2', and 3'. In this way we can consider non-UCO systems, avoid the
doi:10.1109/cdc.2000.914253 fatcat:ioiatmid5rcqjcilhucfx2wyzq