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Autonomous robots commonly aim to complete a nominal behavior while minimizing a cost; this leaves them vulnerable to failure or unplanned scenarios, where a backup or contingency plan to a safe set is needed to avoid a total mission…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
In this paper we investigate the optimal controller synthesis problem, so that the system under the controller can reach a specified target set while satisfying given constraints. Existing model predictive control (MPC) methods learn from a…
We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds…
Reach-avoid analysis is fundamental to reasoning about the safety and goal-reaching behavior of dynamical systems, and serves as a foundation for specifying and verifying more complex control objectives. This paper introduces a reach-avoid…
We propose a method for open-loop stochastic optimal control of LTI systems based on Taylor approximations of quantile functions. This approach enables efficient computation of quantile functions that arise in chance constrained…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…
In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the…
The paper addresses two variants of the stochastic shortest path problem ('optimize the accumulated weight until reaching a goal state') in Markov decision processes (MDPs) with integer weights. The first variant optimizes partial expected…
We consider the control design of stochastic discrete-time linear multi-agent systems (MASs) under a global signal temporal logic (STL) specification to be satisfied at a predefined probability. By decomposing the dynamics into…
In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
Dynamic real-time optimization (DRTO) is a challenging task due to the fact that optimal operating conditions must be computed in real time. The main bottleneck in the industrial application of DRTO is the presence of uncertainty. Many…
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…