Qualitative properties of trajectories of control systems: a survey. (English) Zbl 0951.49003

Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R.

J. Dyn. Control Syst. 1, No. 1, 1-48 (1995).

Summary: We present a unified approach to a complex of related issues in control theory, one based to a great extent on the methods of nonsmooth analysis. The issues include invariance, stability, equilibria, monotonicity, the Hamilton-Jacobi equation, feedback synthesis, and necessary conditions.

MSC:

49-02	Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
49J52	Nonsmooth analysis
34A60	Ordinary differential inclusions
49K15	Optimality conditions for problems involving ordinary differential equations
93B03	Attainable sets, reachability
49L20	Dynamic programming in optimal control and differential games
49N35	Optimal feedback synthesis

Keywords:

weak invariance; strong invariance; local attainability of a set; Lyapounov stability of invariant sets; monotonicity along trajectories; verification functions; Hamiltonian inclusions; necessary conditions; optimal control; nonsmooth analysis; equilibria; Hamilton-Jacobi equation; feedback synthesis

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