Article
Controlling a Class of Nonlinear Systems on Rectangles
Departments of Manuf. & Aerosp. & Mech. Eng., Boston Univ., Brookline, MA
IEEE Transactions on Automatic Control (Impact Factor: 3.17). 12/2006; DOI: 10.1109/TAC.2006.884957 Source: IEEE Xplore

Conference Paper: Optimal control of nondeterministic systems for a computationally efficient fragment of temporal logic
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ABSTRACT: We develop a framework for optimal control policy synthesis for nondeterministic transition systems subject to temporal logic specifications. We use a fragment of temporal logic to specify tasks such as safe navigation, response to the environment, persistence, and surveillance. By restricting specifications to this fragment, we avoid a potentially doublyexponential automaton construction. We compute feasible control policies for nondeterministic transition systems in time polynomial in the size of the system and specification. We also compute optimal control policies for average, minimax (bottleneck), and average costpertaskcycle cost functions. We highlight several interesting cases when optimal policies can be computed in time polynomial in the size of the system and specification. Additionally, we make connections between computing optimal control policies for an average costpertaskcycle cost function and the generalized traveling salesman problem. We give simulation results for motion planning problems.2013 IEEE 52nd Annual Conference on Decision and Control (CDC); 12/2013 
Conference Paper: Bisimilar finite abstractions of stochastic control systems
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ABSTRACT: Abstractionbased approaches to the design of complex control systems construct finitestate models that are formally related to the original control systems, then leverage symbolic techniques from finitestate synthesis to compute controllers satisfying specifications given in a temporal logic, and finally refine the obtained control schemes back to the given concrete complex models. While such approaches have been successfully used to perform synthesis over nonprobabilistic control systems, there are only few results available for probabilistic models: hence the goal of this paper, which considers continuoustime controlled stochastic differential equations. We show that for every stochastic control system satisfying a stochastic version of incremental inputtostate stability, and for every ε > 0, there exists a finitestate abstraction that is εapproximate bisimilar to the stochastic control system (in the sense of moments). We demonstrate the effectiveness of the construction by synthesizing a controller for a stochastic control system with respect to linear temporal logic specifications. Since stochastic control systems are a common mathematical models for many complex safety critical systems subject to uncertainty, our techniques promise to enable a new, automated, correctbyconstruction controller synthesis approach for these systems.2013 IEEE 52nd Annual Conference on Decision and Control (CDC); 12/2013  [Show abstract] [Hide abstract]
ABSTRACT: This paper addresses the motion planning problem using hybrid symbolic techniques. The proposed approach develops a unified hierarchical hybrid control framework using a bismulationbased abstraction technique over the partitioned motion space that can be applied to autonomous aerial robots (3D symbolic motion planning) or ground vehicles (2D symbolic motion planning). The bisimulation relation between the abstracted model and the original continuous system guarantees that their behaviors are the same. This allows to design a discrete supervisor for the abstracted model, and then, the designed supervisor can be applied to the original system while the closedloop behavior does not change. To apply the discrete supervisor to the original continuous system, an interface layer is developed, which on the one hand translates discrete commands of the supervisor to a continuous form applicable to the continuous plant and on the other hand, abstracts the continuous signals of the continuous low layer to discrete symbols understandable by the supervisor. The proposed algorithm is verified through implementation of a hybrid symbolic algorithm for the formation control of unmanned aerial vehicles.Asian Journal of Control 10/2014; · 1.41 Impact Factor
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