Adaptive control of systems represented by partial differential equations and its application to networks of multiagents.

摘要

A long-standing model reference adaptive control transient ill-posedness problem is solved for a class of parabolic and hyperbolic systems with spatially varying coefficients. This ill-posedness, characterized by an almost instant closed-loop state escape, has been arising from setting the initial deviation of the controller parameter values sufficiently far from the ideal ones unknown a priori and/or selecting excessive reference input magnitude or adaptation gain. The closed-loop ill-posedness elimination is accomplished by a removal of the plant state spatial derivatives from the control laws and an appropriate algorithm restructuring. A finite-dimensionalization technique for the controller parameters adaptation laws, based on the multiresolution analysis, is then proposed. This technique permits efficient incorporation of the prior knowledge of the specific plant parameter characteristics, such as nonsmoothness, into controller implementation through the choice of parameter approximation basis, yielding a high fidelity parameter representation by a small number of basis coefficients.; For this purpose, a new tool - the multiresolution Lyapunov functional is introduced. Using the latter, the existence of the wavelet-based finite-dimensional parameter adaptation law providing the desired tracking accuracy, while retaining the well-posedness of the closed-loop system with the infinite-dimensional plant is proven for both parabolic and hyperbolic cases. The benefits of the technique in both real-time and off-line performance enhancement of the control law, such as reduction of computational demand and increase in the output convergence rate unaccompanied by the corresponding increase in the control effort are demonstrated, as well.; The control laws are extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with known parameters or as a spatially-varying time-invariant signal.; Requirement of only local information of the MRAC laws is utilized to extend the control laws developed to MRAC of networks of multiagents. Capability to handle spatially varying parameters means that agents can be heterogeneous. Disturbance rejection scheme is also presented for certain classes of disturbances.