This paper is devoted to determining the viability of hybrid control systems on a region which is expressed by inequalities of piecewise smooth functions. Firstly, the viability condition for the differential inclusion is discussed based on nonsmooth analysis. Secondly, the result is generalized to hybrid differential inclusion. Finally, the viability condition of differential inclusion on a region with the max-type function is given.
This Special Issue of Numerical Algebra, Control and Optimization (NACO) is dedicated to Professor Enmin Feng for his important contributions in Applied Optimization, Optimal Control, System Identification and Large Scale Computing and their Engineering Applications and on the occasion of his 75th Birthday.
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We present a substitution secant/finite difference (SSFD) method
to solve the finite minimax optimization problems with a number
of functions whose Hessians are often sparse, i.e., these matrices are populated
primarily with zeros. By combining of a substitution method,
a secant method and a finite difference method, the gradient
evaluations can be employed as efficiently as possible in forming quadratic
approximations to the functions, which is more effective than that for large sparse unconstrained
Without strict complementarity and linear independence, local and global
convergence is proven and $q$-superlinear convergence result and $r$-convergence rate
estimate show that the method has a good convergence property.
A handling method of a nonpositive definitive Hessian is given
to solve nonconvex problems. Our numerical tests show that the algorithm is robust and quite
effective, and that its performance is comparable to or better than
that of other algorithms available.
In this paper we prove that a postcritically finite rational map with non-empty Fatou set is Thurston equivalent to an expanding Thurston map if and only if its Julia set is homeomorphic to the standard Sierpiński carpet.
In this paper, an optimal control problem for a class of hybrid
systems is considered. By introducing a new time variable and
transforming the hybrid optimal control problem into an equivalent
problem, second order sufficient optimality conditions for this
hybrid problem are derived. It is shown that sufficient optimality
conditions can be verified by checking the Legendre-Clebsch
condition and solving some Riccati equations with certain boundary
and jump conditions. An example is given to show the effectiveness
of the main results.