742 research outputs found
Convex Chance Constrained Model Predictive Control
We consider the Chance Constrained Model Predictive Control problem for
polynomial systems subject to disturbances. In this problem, we aim at finding
optimal control input for given disturbed dynamical system to minimize a given
cost function subject to probabilistic constraints, over a finite horizon. The
control laws provided have a predefined (low) risk of not reaching the desired
target set. Building on the theory of measures and moments, a sequence of
finite semidefinite programmings are provided, whose solution is shown to
converge to the optimal solution of the original problem. Numerical examples
are presented to illustrate the computational performance of the proposed
approach.Comment: This work has been submitted to the 55th IEEE Conference on Decision
and Contro
Data-Driven Chance-Constrained Design of Voltage Droop Control for Distribution Networks
This paper addresses the design of local control methods for voltage control in distribution networks with high levels of distributed energy resources (DERs). The designed control methods modulate the active and reactive power output of DERs proportional to the deviation of the local measured voltage magnitudes from a reference voltage, which is referred to as droop control; thus, the design focuses on determining the droop characteristics that satisfy network-wide voltage magnitude constraints. The uncertainty and variability of DERs renders the design of optimal droop controls very challenging; hence, this paper proposes chance constraints to limit the risk from intermittent DERs by designing droop control coefficients that guarantee the satisfaction of network operational constraints with a specific probability. In addition, the proposed approach relies entirely on historical data rather than assuming knowledge of the probability distributions that characterize the uncertainty of DERs. The efficacy of the proposed method is demonstrated on a 37-bus distribution feeder
Certified Reinforcement Learning with Logic Guidance
This paper proposes the first model-free Reinforcement Learning (RL)
framework to synthesise policies for unknown, and continuous-state Markov
Decision Processes (MDPs), such that a given linear temporal property is
satisfied. We convert the given property into a Limit Deterministic Buchi
Automaton (LDBA), namely a finite-state machine expressing the property.
Exploiting the structure of the LDBA, we shape a synchronous reward function
on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces
that probabilistically satisfy the linear temporal property. This probability
(certificate) is also calculated in parallel with policy learning when the
state space of the MDP is finite: as such, the RL algorithm produces a policy
that is certified with respect to the property. Under the assumption of finite
state space, theoretical guarantees are provided on the convergence of the RL
algorithm to an optimal policy, maximising the above probability. We also show
that our method produces ''best available'' control policies when the logical
property cannot be satisfied. In the general case of a continuous state space,
we propose a neural network architecture for RL and we empirically show that
the algorithm finds satisfying policies, if there exist such policies. The
performance of the proposed framework is evaluated via a set of numerical
examples and benchmarks, where we observe an improvement of one order of
magnitude in the number of iterations required for the policy synthesis,
compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782
Safety Under Uncertainty: Tight Bounds with Risk-Aware Control Barrier Functions
We propose a novel class of risk-aware control barrier functions (RA-CBFs)
for the control of stochastic safety-critical systems. Leveraging a result from
the stochastic level-crossing literature, we deviate from the martingale theory
that is currently used in stochastic CBF techniques and prove that a RA-CBF
based control synthesis confers a tighter upper bound on the probability of the
system becoming unsafe within a finite time interval than existing approaches.
We highlight the advantages of our proposed approach over the state-of-the-art
via a comparative study on an mobile-robot example, and further demonstrate its
viability on an autonomous vehicle highway merging problem in dense traffic.Comment: 7 pages, 4 figures, 5 tables, accepted at ICRA 202
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