Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

Formal controller synthesis for wastewater systems with signal temporal logic constraints: the Barcelona case study

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We present an approach for formal controller synthesis of the Barcelona wastewater system. The goal of the controller is to minimize overflow in the system and to reduce environmental contamination (pollution). Due to the influence of sudden and unpredictable weather changes within the Mediterranean climate, we propose robust model predictive control strategy. This approach synthesizes control inputs (i.e., flows through network actuators) that make the system robust to uncertainties in the weather forecast; control inputs are updated in an online fashion to incorporate the newly available measurements from the system and the disturbances. We employ signal temporal logic as a formal mechanism to express the desired behavior of the system. The quantitative semantics of the logic is then used to encode the desired behavior in both the set of constraints and the objective function of the optimization problem. We propose a solution approach for the obtained worst-case optimization, which is based on transforming the nonlinear dynamics of the system into a mixed logical dynamical model. Then, we employ Monte Carlo sampling and dual reformulation to get a mixed integer linear or quadratic programming problem. The proposed approach is applied to a catchment of the Barcelona wastewater system to illustrate its effectiveness.Peer ReviewedPostprint (author's final draft

Robust model predictive control for an uncertain smart thermal grid

The focus of this paper is on modeling and control of Smart Thermal Grids (STGs) in which the uncertainties in the demand and/or supply are included. We solve the corresponding robust model predictive control (MPC) optimization problem using mixed-integer-linear programming techniques to provide a day-ahead prediction for the heat production in the grid. In an example, we compare the robust MPC approach with the robust optimal control approach, in which the day-ahead production plan is obtained by optimizing the objective function for entire day at once. There, we show that the robust MPC approach successfully keeps the supply-demand balance in the STG while satisfying the constraints of the production units in the presence of uncertainties in the heat demand. Moreover, we see that despite the longer computation time, the performance of the robust MPC controller is considerably better than the one of the robust optimal controller

Robust model predictive control for an uncertain smart thermal grid

The focus of this paper is on modeling and control of Smart Thermal Grids (STGs) in which the uncertainties in the demand and/or supply are included. We solve the corresponding robust model predictive control (MPC) optimization problem using mixed-integer-linear programming techniques to provide a day-ahead prediction for the heat production in the grid. In an example, we compare the robust MPC approach with the robust optimal control approach, in which the day-ahead production plan is obtained by optimizing the objective function for entire day at once. There, we show that the robust MPC approach successfully keeps the supply-demand balance in the STG while satisfying the constraints of the production units in the presence of uncertainties in the heat demand. Moreover, we see that despite the longer computation time, the performance of the robust MPC controller is considerably better than the one of the robust optimal controller

Constrained autonomous satellite docking via differential flatness and model predictive control

We investigate trajectory generation algorithms that allow a satellite to autonomously rendezvous and dock with a target satellite to perform maintenance tasks, or transport the target satellite to a new operational location. We propose different path planning strategies for each of the phases of rendezvous. In the first phase, the satellite navigates to a point in the Line of Sight (LOS) region of the target satellite. We show that the satellite's equations of motion are differentially flat in the relative coordinates, hence the rendezvous trajectory can be found efficiently in the flat output space without a need to integrate the full nonlinear dynamics. In the second phase, we use model predictive control (MPC) with linearized dynamics to navigate the spacecraft to the final docking location within a constrained approach envelope. We demonstrate feasibility of this study by simulating a sample docking mission

Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbances

We present Shrinking Horizon Model Predictive Control (SHMPC) for discrete-time linear systems with Signal Temporal Logic (STL) specification constraints under stochastic disturbances. The control objective is to maximize an optimization function under the restriction that a given STL specification is satisfied with high probability against stochastic uncertainties. We formulate a general solution, which does not require precise knowledge of the probability distributions of the (possibly dependent) stochastic disturbances; only the bounded support intervals of the density functions and moment intervals are used. For the specific case of disturbances that are independent and normally distributed, we optimize the controllers further by utilizing knowledge of the disturbance probability distributions. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for an HVAC system.Comment: 11 pages, 1 figure, 1 table, Submitted to IEEE Transaction on Automatic Control. A limited subset of the results of this paper is accepted for presentation at American Control Conference 201