1. NONLINEAR ADAPTIVE CONTROL RICCARDO MARINO UNIVERSITA DI ROMA TOR VERGATA

2. ADAPTIVE CONTROL OF LINEAR SYSTEMS ADAPTIVE CONTROL OF NONLINEAR SYSTEMS ADAPTIVE CONTROL OF TIME-VARYING SYSTEMS ADAPTIVE DISTURBANCE ATTENUATION/ REJECTION ADAPTIVE REGULATION LEARNING CONTROL NONLINEAR ADAPTIVE CONTROL

3. Adaptive control of linear systems • Given a family of linear time-invariant systems (minimum phase, known upper bound on system order, known relative degree, known sign of high frequency gain), design an output feedback tracking control such that ANY smooth bounded output reference signal is asymptotically tracked from any initial condition with transient specifications: the resulting control is NONLINEAR.

4. Adaptive control of nonlinear systems • Given a family of systems with KNOWN nonlinearities, design an output feedback control which solves an output tracking problem with transient specifications. • If the nonlinearities depend on the measured output, the problem has been solved for a class of nonlinear minimum phase systems which strictly contains the linear ones.

5. The model is required to be LINEARLY parametrized with respect to unknown constant parameters: while this is natural for linear systems, it may be a strong assumption for nonlinear systems. • The control contains parameter estimates which are adapted on the basis of the tracking error. They may or may not converge to the true values depending on persistency of excitation. Nevertheless, asymptotic tracking is achieved.

6. Adaptive control of time- varying systems • Adaptation really means to adapt with respect to system’s time variations and to changes from the environment. • From a technical viewpoint this implies time varying parameters and time varying disturbances and poses many difficulties in adaptive control design: what does adaptation mean if asymptotic tracking cannot be achieved?

7. Adaptive disturbance attenuation/rejection • Given an additive sinusoidal disturbance of unknown frequency acting on a stable/stabilizable system, design an output feedback control which asymptotically rejects the influence of the disturbance on the output. • More generally the disturbance is the sum of a bias and unknown sinusoids.

8. Adaptive regulation • Given a controllable and observable system with additive disturbances and output reference generated by a linear stable exosystem with UNKNOWN parameters, design an output feedback regulator which achieves asymptotic regulation and disturbance rejection.

9. Learning control • Learning control deals with repetitive tasks, i.e. asymptotic tracking of PERIODIC reference signals (and not any smooth bounded as adaptive control does). • The goal of learning control is to learn the unknown reference (periodic) input and not to identify systems parameters.

10. OPEN PROBLEMS IN NONLINEAR ADAPTIVE/LEARNING CONTROL: If the unknown nonlinearities are not linearly parametrized, can we still track a time varying (for instance periodic) reference signal? Can we learn the required reference input? How do we hold the system in the adaptive/learning phase?