6,549 research outputs found
From Uncertainty Data to Robust Policies for Temporal Logic Planning
We consider the problem of synthesizing robust disturbance feedback policies
for systems performing complex tasks. We formulate the tasks as linear temporal
logic specifications and encode them into an optimization framework via
mixed-integer constraints. Both the system dynamics and the specifications are
known but affected by uncertainty. The distribution of the uncertainty is
unknown, however realizations can be obtained. We introduce a data-driven
approach where the constraints are fulfilled for a set of realizations and
provide probabilistic generalization guarantees as a function of the number of
considered realizations. We use separate chance constraints for the
satisfaction of the specification and operational constraints. This allows us
to quantify their violation probabilities independently. We compute disturbance
feedback policies as solutions of mixed-integer linear or quadratic
optimization problems. By using feedback we can exploit information of past
realizations and provide feasibility for a wider range of situations compared
to static input sequences. We demonstrate the proposed method on two robust
motion-planning case studies for autonomous driving
Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)
A new framework is developed for control of constrained nonlinear systems
with structured parametric uncertainties. Forward invariance of a safe set is
achieved through online parameter adaptation and data-driven model estimation.
The new adaptive data-driven safety paradigm is merged with a recent adaptive
control algorithm for systems nominally contracting in closed-loop. This
unification is more general than other safety controllers as closed-loop
contraction does not require the system be invertible or in a particular form.
Additionally, the approach is less expensive than nonlinear model predictive
control as it does not require a full desired trajectory, but rather only a
desired terminal state. The approach is illustrated on the pitch dynamics of an
aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach
implementatio
A receding horizon generalization of pointwise min-norm controllers
Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved
Safety Control Synthesis with Input Limits: a Hybrid Approach
We introduce a hybrid (discrete--continuous) safety controller which enforces
strict state and input constraints on a system---but only acts when necessary,
preserving transparent operation of the original system within some safe region
of the state space. We define this space using a Min-Quadratic Barrier
function, which we construct along the equilibrium manifold using the Lyapunov
functions which result from linear matrix inequality controller synthesis for
locally valid uncertain linearizations. We also introduce the concept of a
barrier pair, which makes it easy to extend the approach to include
trajectory-based augmentations to the safe region, in the style of LQR-Trees.
We demonstrate our controller and barrier pair synthesis method in
simulation-based examples.Comment: 6 pages, 7 figures. Accepted for publication at the 2018 American
Controls Conference. Copyright IEEE 201
Stochastic model predictive control of LPV systems via scenario optimization
A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system's matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios') are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example
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