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Computation of general state- and/or control-constrained Optimal ControlProblems (OCPs) is difficult for various constraints, especially theintractable path constraint. For such problems, the theoretical convergence ofnumerical algorithms is usually not guaranteed, and the right solution may notbe successfully obtained. With the recently proposed Variation Evolving Method(VEM), the evolution equations, which guarantee the convergence towards theoptimal solution in theory even for the general constrained OCPs, are derived.In particular, the costate-free optimality conditions are established. Besidesthe analytic expressions of the costates and the Lagrange multipliers adjoiningthe terminal constraint, the integral equation that determines theKarush-Kuhn-Tucker (KKT) multiplier variable is also derived. Upon the work inthis paper, the general constrained OCPs may be transformed to theInitial-value Problems (IVPs) to be solved, with common Ordinary DifferentialEquation (ODE) numerical integration methods.

Solve the General Constrained Optimal Control Problem with Common Integration Method