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Zbl 0951.49003
Clarke, F.H.; Ledyaev, Yu.S.; Stern, R.J.; Wolenski, P.R.
Qualitative properties of trajectories of control systems: a survey. (English)
[J] J. Dyn. Control Syst. 1, No.1, 1-48 (1995). ISSN 1079-2724; ISSN 1573-8698/e

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 2000:: *49-02 Research monographs (calculus of variations)
49J52 Nonsmooth analysis (other weak concepts of optimality)
34A60 ODE with multivalued right-hand sides
49K15 Optimal control problems with ODE (nec./ suff.)
93B03 Attainable sets
49L20 Dynamic programming method (infinite-dimensional problems)
49N35 Closed-loop controls

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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