Optimality conditions for the minimal time problem for Complementarity Systems

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…• Optimal control: this can a priori be applied to any "classical" system with inputs and sufficient reachability (should it be continuous or discrete-time like a Poincaré mapping). The optimal control of linear complementarity systems, which has been tackled in [345,346,347,348], applies to both dynamics in (55) and (57), and to all robot-object systems with compliant contact. It also applies to the circuits in (72) and (74).…”

“…However research is progressing quickly in this field, where reinforcement learning methods (which are in essence close to optimal control) may bring much [349,350], at least from the computational point of view. Comparisons with more classical optimal control methods which are studied for nonsmooth systems [345,346,347,348], with specific numerical methods [351], will be mandatory in the future. A survey on numerical optimal control for legged robots is proposed in [352].…”

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

“…One important issue lies in the fact that in the non convex case, the biconjugate (ϕ ⋆ ) ⋆ may not equal ϕ, so that manipulations used to invert the set-valued part may no longer be valid (one path could be to use the results in [31]). Other extensions which have not been tackled, could be: consider a mixed LCP instead of an LCP in (2.22) (b), yielding the MLCS: [107] for preliminary results), time-varying LCS with A(t), B(t), C(t), D(t) (see Section 3.4 for a possible path), and control-related issues (optimal control has been tackled in [287,555,554], yielding MPEC problems, with applications in process control [484,96], trajectory tracking, etc). It could be of interest to study the relationships between optimal control of FOSwP tackled in [54,160,162,161,200,202,201,205,316,217,536], which rely on the convergence of a suitable time-discretization or of a regularization of the normal cone, and the results in [555,554], which rely on [287].…”

Optimization of Controlled Free-Time Sweeping Processes with Applications to Marine Surface Vehicle Modeling

“…Nevertheless, within a rather short period of time, many important results have been obtained on necessary optimality conditions for controlled sweeping processes with valuable applications to friction and plasticity, robotics, traffic equilibria, ferromagnetism, hysteresis, economics, and other fields of engineering and applied sciences; see, e.g., [1], [3], [7], [8], [17] with more references and discussions. Let us mention to this end the recent papers [15], [16], where optimal control problems for linear complementarity systems have been studied and applied to practical models that are highly important in the area of Automatic Control. Such problems can be written in a form of controlled sweeping processes, where C is an orthant in R n .…”