Samira S. Farahani

Robust Model Predictive Control for Signal Temporal Logic Synthesis

Abstract 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.

An Approximation Approach for Model Predictive Control of Stochastic Max-Plus Linear Systems

Abstract Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. In previous work we have extended MPC to a class of discrete-event systems, namely the max-plus linear systems, i.e., models that are “lineal” in the max-plus algebra. Lately, the application of MPC for stochastic max-plus-linear systems has attracted a lot of attention. At each event step, an optimization problem then has to be solved that is, in general, a highly complex and computationally hard problem. Therefore, the focus of this paper is on decreasing the computational complexity of the optimization problem. To this end, we use an approximation approach that is based on the p -th raw moments of a random variable. This method results in a much lower computational complexity and computation time while still guaranteeing a good performance.

Exact and approximate approaches to the identification of stochastic max-plus-linear systems

Stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra, belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. In this paper, we study the identification problem for such systems, considering two different approaches. One approach is based on exact computation of the expected values and consists in recasting the identification problem as an optimization problem that can be solved using gradient-based algorithms. However, due to the structure of stochastic max-plus linear systems, this method results in a complex optimization problem. The alternative approach discussed in this paper, is an approximation method based on the higher-order moments of a random variable. This approach decreases the required computation time significantly while still guaranteeing a performance that is comparable to the one of the exact solution.

An approximation method for computing the expected value of max-affine expressions

Abstract Expected values of max-affine expressions appear in optimization problems for various stochastic systems, such as in model predictive control (MPC) for stochastic max-plus-linear systems, in identification of stochastic max-plus-linear systems, and in control of stochastic monotonic piecewise affine systems. Solving these optimization problems involves the computation of the expected value of the maximum of affine expressions, which will then appear in the objective function or in the constraints. The computation of this expected value can be highly complex and expensive, which also results in a high computation time to solve the optimization problem. Therefore, the focus of this paper is on decreasing the computational complexity of the calculation of these expected values. To this end, we use an approximation method based on the moments of a random variable. We illustrate in an example that this method results in a much lower computation time and a much lower computational complexity than the existing computational methods while still guaranteeing a performance that is comparable to the performance of those methods.

Shrinking Horizon Model Predictive Control with chance-constrained signal temporal logic specifications

We present Shrinking Horizon Model Predictive Control (SHMPC) for linear dynamical systems, under stochastic disturbances, with probabilistic constraints encoded as Signal Temporal Logic (STL) specifications. The control objective is to minimize a cost function under the restriction that the given STL specification be satisfied with some minimum probability. The presented approach utilizes the knowledge of the disturbance distribution to synthesize the controller in SHMPC. We show that this synthesis problem can be (conservatively) transformed into sequential optimizations involving linear constraints. We experimentally demonstrate the effectiveness of our proposed approach by evaluating its performance on room temperature control of a building.

Model predictive control for stochastic max-min-plus-scaling systems - an approximation approach

A large class of discrete-event and hybrid systems can be described by a max-min-plus-scaling (MMPS) model, i.e., a model in which the main operations are maximization, minimization, addition, and scalar multiplication. Further, Model Predictive Control (MPC), which is one of the most widely used advanced control design methods in the process industry due to its ability to handle constraints on both inputs and outputs, has already been extended to both deterministic and stochastic MMPS systems. However, in order to compute an MPC controller for a general MMPS system, a nonlinear, nonconvex optimization problem has to be solved. In addition, for stochastic MMPS systems, the problem is computationally highly complex since the cost function is defined as the expected value of an MMPS function and its evaluation leads to a complex numerical integration. The aim of this paper is to decrease this computational complexity by applying an approximation method that is based on the raw moments of a random variable, to a stochastic MMPS system with a Gaussian noise. In this way, the problem can be transformed into a sequence of convex optimization problems, providing that linear or convex MPC input constraints are considered.

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 satellites 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.

Model Predictive Control for Stochastic Switching Max-Plus-Linear Systems

Abstract A switching max-plus-linear system can operate in different modes. In each mode the system is described by a max-plus linear system equation. The switching may depend on the previous mode, on the state, and on the input. Stochastic switching max-plus-linear systems may include two types of stochastic uncertainty, namely stochastic parametric uncertainty and stochastic mode switching uncertainty. For both types of uncertainty results have appeared in the literature. In this paper we will consider stochastic switching max-plus-linear systems with parametric uncertainty and mode switching uncertainty in one single unified framework. First we derive a (general) model that includes both types of stochastic uncertainty. Next a model predictive control method is used to control the system, and we distinguish between the case where the two types of uncertainty are dependent or independent.

An Approximation Approach for Identification of Stochastic Max-Plus Linear Systems

Abstract Max-plus linear systems belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. Our focus in this paper is on stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra. One interesting topic is the identification of such systems. Previous works report on a method for identifying the parameters of a state space model for a stochastic max-plus linear system from measured data. However, due to the structure of such systems, this method results in a complex identification problem. Therefore, the aim of this paper is to decrease the computational complexity and the computation time of this problem. To this end, we use an approximation approach that is based on the higher-order raw moments of a random variable. This method results in a less complex problem that can be solved efficiently using gradient search techniques.

On optimization of stochastic max–min-plus-scaling systems—An approximation approach☆

A large class of discrete-event and hybrid systems can be described by a maxmin-plus-scaling (MMPS) model, i.e., a model in which the main operations are maximization, minimization, addition, and scalar multiplication. Accordingly, optimization of MMPS systems appears in different problems defined for discrete-event and hybrid systems. For a stochastic MMPS system, this optimization problem is computationally highly demanding as often numerical integration has to be used to compute the objective function. The aim of this paper is to decrease such computational complexity by applying an approximation method that is based on the moments of a random variable and that can be computed analytically.