Model Predictive Control for Systems with Partially Unknown Dynamics Under Signal Temporal Logic Specifications

Abstract

Autonomous systems are seeing increased deployment in real-world applications such as self-driving vehicles, package delivery drones, and warehouse robots. In these applications, such systems are often required to perform complex tasks that involve multiple, possibly inter-dependent steps that must be completed in a specific order or at specific times. One way of mathematically representing such tasks is using temporal logics. Specifically, Signal Temporal Logic (STL), which evaluates real-valued, continuous-time signals, has been used to formally specify behavioral requirements for autonomous systems.

This thesis proposes a design for a Model Predictive Controller (MPC) for systems to satisfy STL specifications when the system dynamics are partially unknown, and only a nominal model and past runtime data are available. The proposed approach uses Gaussian Process (GP) regression to learn a stochastic, data-driven model of the unknown dynamics, and manages uncertainty in the STL specification resulting from the stochastic model using Probabilistic Signal Temporal Logic (PrSTL). The learned model and PrSTL specification are then used to formulate a chance-constrained MPC. For systems with high control rates, a modification is discussed for improving the solution speed of the control optimization. In simulation case studies, the proposed controller increases the frequency of satisfying the STL specification compared to controllers that use only the nominal dynamics model. An initial design is also proposed that extends the controller to distributed multi-agent systems, which must make individual decisions to complete a cooperative task.