The course concerns the analysis and synthesis of nonlinear control systems and it has been designed in order to provide the student with the basic knowledge and understanding of nonlinear systems, their stability and basic control design methods.
1.understanding the basic properties of nonlinear systems
2.knowledge of Lyapunov stability theory, absolute stability and passivity.
3.Knowledge and skills in designing simple controllers utilizing Lyapunov theory
4.Knowledge and skills in the utilization of input state and input-output feedback linearizing techniques and in the design of sliding mode and adaptive controllers.
Course Content (Syllabus)
-Overview of the basic properties of nonlinear systems, equilibrium points, second order systems: phase plane analysis, examples of nonlinear systems.
-Lyapunov stability in autonomous systems: definitions and theorems, Definition of invariant sets and convergence, LaSalle theorem, regions of attractions, linearization of nonlinear systems, indirect Lyapunov method, instability theorems
-Lyapunov stability in nonautonomous systems: definitions and theorems, linear time varying systems, perturbation analysis, converse theorems, stability of discrete-time systems
-Feedback systems, basic feedback stabilization, integrator backstepping
-input/output stability, small gain theorem, absolute stability theorems (Popov and circle criteria), input to state stability.
-Passivity, passive systems interconnection, hyperstability theorems
-Model reference adaptive control
Additional bibliography for study
1) Applied Nonlinear Control, 1991, Prentice Hall, Slotine J.-J. E. (Jean-Jacques E.), Li Weiping ISBN:0130408905. 2) Nonlinear Systems, 2002, Prentice Hall, Khalil Hassan K. ISBN:0130673897 , 3rd Edition.