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14:00 | Mixed-Integer Formulations for Optimal Control of Piecewise-Affine Systems ABSTRACT. In this paper we study how to formulate the optimal control problem for a piecewise-affine dynamical system as a mixed-integer program. Problems of this form arise typically in hybrid Model Predictive Control (MPC), where at every time step an open-loop optimal control sequence is computed via numerical optimization and applied to the system in a moving horizon fashion. Not surprisingly, the efficiency in the formulation of the underlying mathematical program has a crucial influence on computation times, and hence on the applicability of hybrid MPC to high-dimensional systems. We leverage on modern concepts and results from the fields of mixed-integer and disjunctive programming to conduct a comprehensive analysis of this formulation problem: among the outcomes enabled by this novel perspective is the derivation of multiple highly-efficient formulations of the control problem, each of which represents a different tradeoff between the two most important features of a mixed-integer program, the size and the strength. First in theory, then through a numerical example, we show how all the proposed methods outperform the traditional approach employed in MPC, enabling the solution of larger-scale problems. |

14:30 | Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems ABSTRACT. This work targets the development of a scalable abstraction method for formal analysis and control synthesis of discrete-time stochastic hybrid systems (SHS) with linear dynamics. The focus is on linear-time specifications, both over finite and infinite time horizons. The framework constructs a finite abstraction as an interval Markov decision process (IMDP). Then, a strategy maximizing the satisfaction probability of the given specification is synthesized over the IMDP and mapped to the underlying SHS. In contrast to existing formal approaches, by and large limited to finite-time properties and relying on conservative over-approximations, we show that the exact abstraction error is computed as a solution of convex optimization problems, and embedded into the IMDP abstraction: this allows for the quantification of the exact abstraction errors for finite- and infinite-horizon specifications, which is later used in the synthesis step. This mitigates the known state-space explosion problem: our experimental validation shows improved scalability compared to existing approaches. |

15:00 | pFaces: An Acceleration Ecosystem for Symbolic Control SPEAKER: Mahmoud Khaled ABSTRACT. The correctness of control software in many safety-critical applications such as autonomous vehicles is crucial. One technique to achieve correct control software is called "symbolic control", where complex systems are approximated by finite-state abstractions. Then, using those abstractions, provably-correct digital controllers are algorithmically synthesized for concrete systems, satisfying complex high-level requirements. Unfortunately, the complexity of synthesizing such controllers grows exponentially in the number of state variables. However, if distributed implementations are considered, high-performance computing platforms can be leveraged to mitigate the effects of the state-explosion problem. We propose pFaces, an extensible software-ecosystem, to accelerate symbolic control techniques. It facilitates designing parallel algorithms and supervises their executions to utilize available computing resources. To demonstrate its capabilities, novel parallel algorithms are designed for abstraction-based controller synthesis. Then, they are implemented inside pFaces and dispatched, for parallel execution, in different heterogeneous computing platforms, including CPUs, GPUs and Hardware Accelerators (HWAs). Results show remarkable reduction in the computation time by several orders of magnitudes as number of processing elements (PEs) increases, which outperforms easily all the existing tools. |

15:15 | Business Meeting |