Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

Model Predictive Control Based Energy Management Algorithm for a Hybrid Excavator

The Volvo Group has an ambitious plan to efficiencies its construction equipment vehicles with an introduction of a hybrid engine. This Master thesis is based on, as a first approach, to control the energy split in a hybrid construction equipment vehicle (HCEV) with the control strategy Model Predictive Control (MPC). The work is divided into two main parts, where the first one is to create a piece-wise affine system (PWA) of the nonlinear plant and secondly to define the control strategy. Multiple linear models are created from the different mathematical descriptions with the Taylor expansion and then divided in space with polytopes to represent the hybrid dynamics properly. After that, the MPC strategy is to be created and this is done by defining a cost function, where selected variables should follow some trajectory. At each sample, the MPC controller should compute an optimal control signal during the prediction and control horizon to minimize the fuel consumption, make the internal combustion engine run at a favourable rotational speed and save the durability on the battery. The control problem is simulated in Simulink with a pre-defined driving cycle, as can be seen as an artificial user for the HCEV, which generates a power demand that needs to be satisfie

Error Bounds for Piecewise Smooth and Switching Regression

The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switching laws. The paper derives generalization error bounds in these two settings by following the approach based on Rademacher complexities. For PWS regression, our derivation involves a chaining argument and a decomposition of the covering numbers of PWS classes in terms of the ones of their component functions and the capacity of the classifier partitioning the input space. This yields error bounds with a radical dependency on the number of modes. For switching regression, the decomposition can be performed directly at the level of the Rademacher complexities, which yields bounds with a linear dependency on the number of modes. By using once more chaining and a decomposition at the level of covering numbers, we show how to recover a radical dependency. Examples of applications are given in particular for PWS and swichting regression with linear and kernel-based component functions.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice,after which this version may no longer be accessibl

Formal methods for resilient control

Many systems operate in uncertain, possibly adversarial environments, and their successful operation is contingent upon satisfying specific requirements, optimal performance, and ability to recover from unexpected situations. Examples are prevalent in many engineering disciplines such as transportation, robotics, energy, and biological systems. This thesis studies designing correct, resilient, and optimal controllers for discrete-time complex systems from elaborate, possibly vague, specifications. The first part of the contributions of this thesis is a framework for optimal control of non-deterministic hybrid systems from specifications described by signal temporal logic (STL), which can express a broad spectrum of interesting properties. The method is optimization-based and has several advantages over the existing techniques. When satisfying the specification is impossible, the degree of violation - characterized by STL quantitative semantics - is minimized. The computational limitations are discussed. The focus of second part is on specific types of systems and specifications for which controllers are synthesized efficiently. A class of monotone systems is introduced for which formal synthesis is scalable and almost complete. It is shown that hybrid macroscopic traffic models fall into this class. Novel techniques in modular verification and synthesis are employed for distributed optimal control, and their usefulness is shown for large-scale traffic management. Apart from monotone systems, a method is introduced for robust constrained control of networked linear systems with communication constraints. Case studies on longitudinal control of vehicular platoons are presented. The third part is about learning-based control with formal guarantees. Two approaches are studied. First, a formal perspective on adaptive control is provided in which the model is represented by a parametric transition system, and the specification is captured by an automaton. A correct-by-construction framework is developed such that the controller infers the actual parameters and plans accordingly for all possible future transitions and inferences. The second approach is based on hybrid model identification using input-output data. By assuming some limited knowledge of the range of system behaviors, theoretical performance guarantees are provided on implementing the controller designed for the identified model on the original unknown system

Machine learning and data-driven techniques for verification and synthesis of cyber-physical systems

Safety and performance are the most important requirements for designing and manufacturing complex life-critical systems. Consider a self-driving car which is not equipped with certain safety functionalities. It can cause fatal accidents, severe injuries, or serious damages to the environment. Hence, rigorous analysis required to ensure the correctness of functionalities in many safety-critical applications. Model-based approaches for satisfying such requirements have been studied extensively in the literature. Unfortunately, a precise model of the system is not always available in many practical scenarios. Hence, in this thesis we focus on data-driven methods and machine learning techniques to tackle this challenge. First, we assume that only an incomplete parameterized model of the system is available. The main goal is to study formal verification of linear time-invariant systems with respect to a fragment of temporal logic specifications when only a partial knowledge of the model is available, i.e., a parameterized model of the system is known but the exact values of the parameters are unknown. We provide a probabilistic measure for the satisfaction of the specification by trajectories of the system under the influence of uncertainty. We assume that these specifications are expressed as signal temporal logic formulae and provide an approach that relies on gathering input-output data from the system. We employ Bayesian inference on the collected data to associate a notion of confidence with the satisfaction of the specification. Second, we assume that we do not have any knowledge about the model of the system and just have access to input-output data from the system. We study verification and synthesis problems for safety specifications over unknown discrete-time stochastic systems. When a model of the system is available, notion of barrier certificates have been successfully applied for ensuring the satisfaction of safety specifications. Here, we formulate the computation of barrier certificates as a robust convex program (RCP). Solving the acquired RCP is difficult in general because the model of the system that appears in one of the constraints of the RCP is unknown. We propose a data-driven approach that replaces the uncountable number of constraints in the RCP with a finite number of constraints by taking finitely many random samples from the trajectories of the system. We thus replace the original RCP with a scenario convex program (SCP) and show how to relate their optimizers. We guarantee that the solution of the SCP is a solution of the RCP with a priori guaranteed confidence when the number of samples is larger than a specific value. This provides a lower bound on the safety probability of the original unknown system together with a controller in the case of synthesis. Lastly, to address the high demand for data in our data-driven barrier-based approach, we propose three remedies. First, the wait-and-judge approach that checks a condition over the optimal value of the SCP using a fixed number of samples, ensuring a lower bound probability and the desired confidence for satisfying safety specifications. Second, the repetition-based scenario framework that iteratively solves the SCP with samples, checking feasibility and achieving the desired violation error. A safety condition is verified, enabling the computation of a lower bound for safety satisfaction. Third, the wait, judge, and repeat framework that solves the SCP iteratively until a feasibility condition, based on computed support constraints, is met. If the safety condition is satisfied, the system is considered safe with a lower bound probability determined using the optimizer of the successful iteration