There are many situations for which a feasible nonholonomic motion plan must be generated immediately based on real-time perceptual information. Parametric trajectory representations limit computation because they reduce the search space for solutions (at the cost of potentially introducing suboptimality). The use of any parametric trajectory model converts the optimal control formulation into ...

The design of robust time-optimal controllers using the sensitivity concept is presented in this paper. A parameter optimization problem is solved using the Switch Time Optimization algorithm to determine a bang-bang control profile that minimizes the maneuver time subject to the constraint that the sensitivity of the final states with respect to system parameters are zero. The proposed approac...

We present two algebraic methods to solve the parametric optimization problem that arises in nonlinear model predictive control. We consider constrained discrete-time polynomial systems and the corresponding constrained finite-time optimal control problem. The first method is based on cylindrical algebraic decomposition. The second uses Gröbner bases and the eigenvalue method for solving system...

Parametric optimal control problems for semilinear parabolic equations are considered. Using recent Lipschitz stability results for solutions of such problems, it is shown that, under standard coercivity conditions, the solutions are Bouligand differentiable (in L, p < ∞) functions of the parameter. The differentials are characterized as the solutions of accessory linear-quadratic problems. A u...

The problem of effectively adiabatic control of a collection of classical harmonic oscillators sharing the same time-dependent frequency is analyzed. The phase differences between the oscillators remain fixed during the process. This fact leads us to adopt the coordinates: energy, Lagrangian, and correlation, which have proved useful in a quantum description and which have the advantage of trea...

This paper presents biped walking control using a library of optimal trajectories. The biped walking control problem is formulated as an optimal control problem. We take advantage of a parametric trajectory optimization method to find the periodic steady-state trajectory in regular walking. Then we use Differential Dynamic Programming (DDP) to generate a library of optimal trajectories and loca...

We study parametric optimal control problems governed by a system of timedependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute optimal control functions and so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of opt...