Economic MPC of Nonlinear Systems with Non-Monotonic Lyapunov Functions and Its Application to HVAC Control

This paper proposes a Lyapunov-based economic MPC scheme for nonlinear sytems with non-monotonic Lyapunov functions. Relaxed Lyapunov-based constraints are used in the MPC formulation to improve the economic performance. These constraints will enforce a Lyapunov decrease after every few steps. Recursive feasibility and asymptotical convergence to the steady state can be achieved using Lyapunov-like stability analysis. The proposed economic MPC can be applied to minimize energy consumption in HVAC control of commercial buildings. The Lyapunov-based constraints in the online MPC problem enable the tracking of the desired set-point temperature. The performance is demonstrated by a virtual building composed of two adjacent zones

Analysis and design of model predictive control frameworks for dynamic operation -- An overview

This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference signals to the general economic operation of a plant under online changing time-varying operating conditions. We focus on the particular challenges that arise when dealing with such more general control goals and present methods that have emerged in the literature to address these issues. The goal of this article is to present an overview of the state-of-the-art techniques, providing a diverse toolkit to apply and further develop MPC formulations that can handle the challenges intrinsic to dynamic operation. We also critically assess the applicability of the different research directions, discussing limitations and opportunities for further researc

Computational Optimizations for Machine Learning

The present book contains the 10 articles finally accepted for publication in the Special Issue “Computational Optimizations for Machine Learning” of the MDPI journal Mathematics, which cover a wide range of topics connected to the theory and applications of machine learning, neural networks and artificial intelligence. These topics include, among others, various types of machine learning classes, such as supervised, unsupervised and reinforcement learning, deep neural networks, convolutional neural networks, GANs, decision trees, linear regression, SVM, K-means clustering, Q-learning, temporal difference, deep adversarial networks and more. It is hoped that the book will be interesting and useful to those developing mathematical algorithms and applications in the domain of artificial intelligence and machine learning as well as for those having the appropriate mathematical background and willing to become familiar with recent advances of machine learning computational optimization mathematics, which has nowadays permeated into almost all sectors of human life and activity

Optimization Based Control for Multi-agent System with Interaction

Recently, the artificial intelligence has achieved a significant success with applications in various domains including transportation, smart building, robotics, economy and so on. More and more traditional system entities have been entitled with full or partial autonomy, allowing them to make their own decisions and moves based on the specific surrounding environments. An integration of multiple such intelligent entities is called a multi-agent system (MAS) where the agents need to interact with each other effectively and efficiently to attain cooperation and optimal system performance. As to fulfill this more challenging intelligent interaction objective, the traditional control approaches will not suffice and more advanced algorithms become essential.In this dissertation, three system structures for interactive control systems, centralized, distributed and decentralized, are discussed with application in intelligent building and autonomous driving. Several concrete interactive control algorithms are proposed and verified.In the centralized control system, a single central agent with the whole system information available is in charge of making decisions for all the agents. The systemwise cooperation solution is thus directly obtained and all the interactions involved are optimally addressed. Chapter 3 and 4 adopt such centralized control strategy for the intelligent building system. In order to save energy consumption and satisfy the occupants' thermal comfort demand, a combination of feedforward iterative learning control (ILC) and iteratively tuned feedback controller is designed to compensate both repetitive and non-repetitive disturbance components. Chapter 3 proposes an iterative controller design algorithm via optimization solving and stabilizing feedback projection. In Chapter 4, the concurrent design of feedforward ILC and causal stabilizing feedback controller is introduced, where both controllers are simultaneously solved by one optimization.However, the centralized approach's complexity grows with the problem size, which leads to failure for large-scale systems. The distributed control strategy is introduced as an alternative for such high-dimensional control problems. In the distributed system, a communication network enables the information exchange among agents. Therefore, each agent can keep broadcasting and updating its local controller until a convergence to the cooperative solution is reached. In Chapter 5, a distributed cooperative controller design method is developed for intelligent building thermal control with convergence property theoretically proven.For a system with no global communication, agents of which follow different control policies, the decentralized control structure is the only valid solution, where each agent designs its local controller independently based on estimated information of others. In Part II of the dissertation, several decentralized interactive control algorithms are proposed for the autonomous driving system. In Chapter 6, an optimization-based negotiation with both concession and persuasion is formulated for vehicle agent's decision making in various interactive scenarios. A Bayesian persuasion based algorithm for interactive driving is explored in Chapter 7. In the algorithm, the ego vehicle agent (persuader) intends to manipulate the interacting vehicle agent (information receiver)'s belief about the current driving situation via observable driving behavior. In Chapter 8, the interaction between two vehicle agents is defined as a two-player persuasion game, the mixed Nash equilibrium of which denotes the agents' optimal intention probabilities. The optimal intention is then expressed via the ego vehicle's driving trajectory planned by an optimization with the intention expression constraint

Green Scheduling of Control Systems

Electricity usage under peak load conditions can cause issues such as reduced power quality and power outages. For this reason, commercial electricity customers are often subject to demand-based pricing, which charges very high prices for peak electricity demand. Consequently, reducing peaks in electricity demand is desirable for both economic and reliability reasons. In this thesis, we investigate the peak demand reduction problem from the perspective of safe scheduling of control systems under resource constraint. To this end, we propose Green Scheduling as an approach to schedule multiple interacting control systems within a constrained peak demand envelope while ensuring that safety and operational conditions are facilitated. The peak demand envelope is formulated as a constraint on the number of binary control inputs that can be activated simultaneously. Using two different approaches, we establish a range of sufficient and necessary schedulability conditions for various classes of affine dynamical systems. The schedulability analysis methods are shown to be scalable for large-scale systems consisting of up to 1000 subsystems. We then develop several scheduling algorithms for the Green Scheduling problem. First, we develop a periodic scheduling synthesis method, which is simple and scalable in computation but does not take into account the influence of disturbances. We then improve the method to be robust to small disturbances while preserving the simplicity and scalability of periodic scheduling. However the improved algorithm usually result in fast switching of the control inputs. Therefore, event-triggered and self-triggered techniques are used to alleviate this issue. Next, using a feedback control approach based on attracting sets and robust control Lyapunov functions, we develop event-triggered and self-triggered scheduling algorithms that can handle large disturbances affecting the system. These algorithms can also exploit prediction of the disturbances to improve their performance. Finally, a scheduling method for discrete-time systems is developed based on backward reachability analysis. The effectiveness of the proposed approach is demonstrated by an application to scheduling of radiant heating and cooling systems in buildings. Green Scheduling is able to significantly reduce the peak electricity demand and the total electricity consumption of the radiant systems, while maintaining thermal comfort for occupants