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We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that...
This paper provides analytical results regarding the stability of linear discrete-time systems with stochastic delays. Necessary and sufficient stability conditions are derived by using the second moment dynamics which can be used to draw stability charts. The results are applied to a simple connected vehicle system where the stability regions are compared to those given by the mean dynamics. Our...
We present a method for mending strategies for GR(1) specifications. Given the addition or removal of edges from the game graph describing a problem (essentially transition rules in a GR(1) specification), we apply a μ-calculus formula to a neighborhood of states to obtain a “local strategy” that navigates around the invalidated parts of an original synthesized strategy. Our method may thus avoid...
The cost of the great expressivity of motion planning subject to temporal logic formulae is intractability. Recent advances in sampling-based methods seem to be only applicable to “low-level” control. The problem of realizing “high-level” controllers that satisfy a temporal logic specification does not readily admit approximations, unless the notion of correctness is relaxed as might be achieved with...
This paper investigates the stability of linear systems with stochastic delay in discrete time. Stability of the mean and second moment of the non-deterministic system is determined by a set of deterministic discrete-time equations with distributed delay. A theorem is provided that guarantees convergence of the state with convergence of the second moment, assuming that delays are identically independently...
We propose a procedure for the synthesis of control protocols for systems governed by nonlinear differential equations and constrained by temporal logic specifications. This procedure relies on a particular finite-state abstraction of the underlying continuous dynamics and a discrete representation of the external environmental signals. A two-player game formulation provides computationally efficient...
The motion of microorganisms as well as of tiny robotic swimmers for biomedical applications is governed by low Reynolds number (Re) hydrodynamics, where viscous effects dominate and inertial effects are negligible. This paper presents experimental results that verify theoretical predictions of our recent work which analyzed the dynamics and stability of a low-Re swimmer near a plane wall. The experimental...
This paper investigates the convergence rates of several controllers for low dimenional nonholonomic systems in power form. The method of multiple scales is found to be effective in determining the asymptotic form of the solutions. The general form of the perturbation solutions indicates how parameters in the control laws may be chosen to achieve a desired convergence rate. A detailed analysis of...
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