636 research outputs found

    Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants

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    In this paper, we propose a new method for ensuring formally that a controlled trajectory stay inside a given safety set S for a given duration T. Using a finite gridding X of S, we first synthesize, for a subset of initial nodes x of X , an admissible control for which the Euler-based approximate trajectories lie in S at t ∈\in [0,T]. We then give sufficient conditions which ensure that the exact trajectories, under the same control, also lie in S for t ∈\in [0,T], when starting at initial points 'close' to nodes x. The statement of such conditions relies on results giving estimates of the deviation of Euler-based approximate trajectories, using one-sided Lipschitz constants. We illustrate the interest of the method on several examples, including a stochastic one

    Reachability-based Identification, Analysis, and Control Synthesis of Robot Systems

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    We introduce reachability analysis for the formal examination of robots. We propose a novel identification method, which preserves reachset conformance of linear systems. We additionally propose a simultaneous identification and control synthesis scheme to obtain optimal controllers with formal guarantees. In a case study, we examine the effectiveness of using reachability analysis to synthesize a state-feedback controller, a velocity observer, and an output feedback controller.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

    Robust model predictive control: robust control invariant sets and efficient implementation

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    Robust model predictive control (RMPC) is widely used in industry. However, the online computational burden of this algorithm restricts its development and application to systems with relatively slow dynamics. We investigate this problem in this thesis with the overall aim of reducing the online computational burden and improving the online efficiency. In RMPC schemes, robust control invariant (RCI) sets are vitally important in dealing with constraints and providing stability. They can be used as terminal (invariant) sets in RMPC schemes to reduce the online computational burden and ensure stability simultaneously. To this end, we present a novel algorithm for the computation of full-complexity polytopic RCI sets, and the corresponding feedback control law, for linear discrete-time systems subject to output and initial state constraints, performance bounds, and bounded additive disturbances. Two types of uncertainty, structured norm-bounded and polytopic uncertainty, are considered. These algorithms are then extended to deal with systems subject to asymmetric initial state and output constraints. Furthermore, the concept of RCI sets can be extended to invariant tubes, which are fundamental elements in tube based RMPC scheme. The online computational burden of tube based RMPC schemes is largely reduced to the same level as model predictive control for nominal systems. However, it is important that the constraint tightening that is needed is not excessive, otherwise the performance of the MPC design may deteriorate, and there may even not exist a feasible control law. Here, the algorithms we proposed for RCI set approximations are extended and applied to the problem of reducing the constraint tightening in tube based RMPC schemes. In order to ameliorate the computational complexity of the online RMPC algorithms, we propose an online-offline RMPC method, where a causal state feedback structure on the controller is considered. In order to improve the efficiency of the online computation, we calculate the state feedback gain offline using a semi-definite program (SDP). Then we propose a novel method to compute the control perturbation component online. The online optimization problem is derived using Farkas' Theorem, and then approximated by a quadratic program (QP) to reduce the online computational burden. A further approximation is made to derive a simplified online optimization problem, which results in a large reduction in the number of variables. Numerical examples are provided that demonstrate the advantages of all our proposed algorithms over current schemes.Open Acces

    Risk-aware motion planning for automated vehicle among human-driven cars

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    We consider the maneuver planning problem for automated vehicles when they share the road with human-driven cars and interact with each other using a finite set of maneuvers. Each maneuver is calculated considering input constraints, actuator disturbances and sensor noise, so that we can use a maneuver automaton to perform higher-level planning that is robust against lower-level effects. In order to model the behavior of human-driven cars in response to the intent of the automated vehicle, we use control improvisation to build a probabilistic model. To accommodate for potential mismatches between the learned human model and human driving behaviors, we use a conditional value-at-risk objective function to obtain the optimal policy for the automated vehicle. We demonstrate through simulations that our motion planning framework consisting of an interactive human driving model and risk-aware motion planning strategy makes it possible to adapt to different traffic conditions and confidence levels
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