Minimax Control Research Articles

Distributed Minmax Strategy for Multiplayer Games: Stability, Robustness, and Algorithms.

This article studies a distributed minmax strategy for multiplayer games and develops reinforcement learning (RL) algorithms to solve it. The proposed minmax strategy is distributed, in the sense that it finds each player's optimal control policy without knowing all the other players' policies. Each player obtains its distributed control policy by solving a distributed algebraic Riccati equation in a multiplayer noncooperative game. This policy is found against the worst policies of all the other players. We guarantee the existence of distributed minmax solutions and study their L2 and asymptotic stabilities. Under mild conditions, the resulting minmax control policies are shown to improve robust gain and phase margins of multiplayer systems compared to the standard linear-quadratic regulator controller. Distributed minmax solutions are found using both model-based policy iteration and data-driven off-policy RL algorithms. Simulation examples verify the proposed formulation and its computational efficiency over the nondistributed Nash solutions.

A Cross-Layer Game-Theoretic Approach to Resilient Control of Networked Switched Systems Against DoS Attacks.

This article investigates the resilient control strategies of networked switched systems (NSSs) against denial-of-service (DoS) attacks and external disturbance. In the network layer, both the defender and the attacker allocate energy over multiple channels. Considering the impact of switching characteristic in the physical layer on the network layer, a dynamic regulating factor is proposed to adjust the total energy of the defender. To optimize the signal-to-interference-noise ratio and energy consumption simultaneously at each player's side, a multiobjective game problem is formulated. Furthermore, a nondominated sorting genetic algorithm framework is employed, incorporating the knee point selection mechanism to attain the Pareto-Nash equilibrium, based on which the optimal defense strategy can be derived to achieve resilience against DoS attacks. In the physical-layer, taking the dynamic packet loss caused by DoS attacks and external disturbance into account, an H∞ minimax controller containing control inputs and the switching signal is designed to guarantee the optimal performance for NSSs through the dynamic game-theoretic approach. Finally, the networked continuous stirred tank reactor system is provided to verify the effectiveness of the proposed method.

Идентификация параметров агент-ориентированной модели управления промышленным комплексом региона

Current challenges facing the Russian economy require models to optimise industrial management processes at the regional level. Therefore, a three-level hierarchical agent-based model for minimax control of the regional industrial complex is considered in this research. The study aims to develop an approach to solving a parameter identification problem of the agent-based model for managing the industrial complex of Sverdlovsk oblast. To this end, the paper presents a theoretical justification for the implemented approach, a formalisation of the aforementioned problem, and an algorithm for constructing and selecting models to assess management system parameters. The method of linear regression analysis was applied to solve the identification problem. The proposed approach was tested using data on 28 types of industrial activity in Sverdlovsk oblast for 2005–2021. The phase vector of statistical identification models was defined by the following parameters: the average annual number of employees of enterprises; fixed assets; gross value added; volume of shipped goods, performed works and services; balanced financial results of enterprises; investment in fixed capital; costs of implementing and using digital technologies. The control vector was determined by the factors of attracting budgetary and other (external) funds. As a result, 125 high-quality models were built to solve parameter identification problems of the agent-based model used for managing the industrial complex of Sverdlovsk oblast. The obtained statistical models can be used to establish communication between agents, clarify their specificity, calculate and assess management performance. The proposed approach can be applied to predict the development of regional industrial complexes in accordance with planned control actions, as well as to calculate control actions necessary to achieve target parameters.

The H∞‐optimal control problem of CSVIU systems

AbstractThe article devises an ‐norm theory for the CSVIU (control and state variations increase uncertainty) class of stochastic systems. This system model appeals to stochastic control problems to express the state evolution of a possibly nonlinear dynamic system restraint to poor modeling. It introduces the control with infinity energy disturbance signals, contrary to usual stochastic formulations, which mimic deterministic models dealing with finite energy disturbances. The reason is to portray the persistent perturbations due to the environment more naturally. In this regard, it develops a refined connection between a notion of stability and the system's power finiteness. It delves into the control solution employing the relations between optimization and differential games, connecting the worst‐case stability analysis of CSVIU systems with a perturbed Lyapunov type of equation. The norm characterization relies on the optimal cost induced by the min–max control strategy. The solvability of a generalized game‐type Riccati equation couples to the rise of a pure saddle point, yielding the global solution of the CSVIU dynamic game. In the way to the optimal stabilizing compensator, the article finds it based on linear feedback stabilizing gain from solving the Riccati equation together with a spectral radius test of an ensuing matrix. The optimal disturbance compensator produces inaction regions in the sense that, for sufficiently minor deviations from the model, the optimal action is constant or null in the face of the uncertainty involved. Finally, an explicit solution approximation developed by a Monte Carlo method appears, and a numerical example illustrates the synthesis.

On Strategic Measures and Optimality Properties in Discrete-Time Stochastic Control with Universally Measurable Policies

This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these systems. The results are then applied to risk-neutral and risk-sensitive Markov decision processes to establish the measurability of the optimal value functions and the existence of universally measurable, randomized or nonrandomized, ϵ-optimal policies, for a variety of average cost criteria and risk criteria. We also extend our analysis to a class of minimax control problems and establish similar optimality results under the axiom of analytic determinacy. Funding: This work was supported by grants from DeepMind, the Alberta Machine Intelligence Institute (AMII), and Alberta Innovates-Technology Futures (AITF).

Optimal feedback control law for automated vehicles in the presence of cyberattacks: A min–max approach

While automated vehicles (AVs) are expected to bring a wide range of benefits to future transportation systems, emerging AV technologies open a door for cyberattacks, where a select number of AVs are compromised to drive in an adversarial manner. This could result in network-wide increases in traffic congestion and energy consumption, degrading the performance of transportation systems. Hence, it is necessary to develop attack mitigation strategies for AVs as AVs gradually become a reality. However, this is rather challenging due to the lack of knowledge of adversaries. Limited prior studies have assumed attacks with a given probability distribution without considering their malicious intention, which is far from realistic due to the adversarial nature of potential attacks.In this study, we derive an optimal feedback control law for AVs in the presence of cyberattacks. Notably, attacks are only assumed to have a bounded magnitude without being subject to any specific statistical distribution, which is not only of theoretical interest but also relaxes the assumptions seen in prior studies. More importantly, to deal with lack of knowledge of malicious attacks, we, for the first time, formulate a min–max control problem to minimize the worst-case disturbance to traffic flow. Specifically, we present a mathematical framework for describing mixed-autonomy traffic involving AVs and human-driven vehicles (HVs), considering two typical types of attacks, namely false data injection attack on sensor measurements and malicious attack on AV control commands. Based on the framework presented, we derive a set of necessary conditions of optimality for the min–max control problem, based on which an iterative computational algorithm is developed for determining the optimal control (driving) strategy of AVs. The effectiveness of the proposed approach is demonstrated via extensive numerical simulations.

A new application of the hardware in the loop test of the min–max controller for turbofan engine fuel control

AbstractThis article performs a novel hardware test application on the min–max algorithm to control a two‐axis turbofan engine's fuel with a high bypass ratio. In this technique the microcontroller uses a nonlinear model based on the min–max algorithm to control the turbofan's fuel consumption. The min–max control method precisely provides the desired thrust while meeting the engine's physical and operational limitations. By setting the engine's limits appropriately, a surge is prevented from happening due to overheating of the turbine. As a proof of concept, the proposed fuel control algorithm is verified using an Intel Addison's Arduino microcontroller connected to a computer. The implemented hardware is examined by incorporating it into a typical control loop test and monitored via a computer. The achieved results indicate fast time response and algorithm flexibility in simulation modes. The test results confirm the precision and proper implementation of the proposed min–max control algorithm. In addition, the suggested min–max control algorithm can be applied to realize restrictions such as the rotational speed and the outlet pressure of the high‐pressure compressor under the required conditions.

On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems

On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems

Minimax Q-learning control for linear systems using the Wasserstein metric

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear systems and adopt a Wasserstein penalty to address the distribution uncertainty of additive stochastic disturbances. By constructing an equivalent deterministic game of the penalized LQR problem, we propose a Q-learning method with convergence guarantees to learn an optimal minimax controller.

Reduced-Order Min-Max Guaranteed Cost Control for Finite-Time Boundedness of Uncertain Linear Systems Using Output Feedback

This letter considers a problem of designing reduced-order dynamic output feedback controllers for finite-time boundedness of uncertain linear time-varying systems subjected to exogenous disturbances. Differential linear matrix inequality conditions are derived for finite-time boundedness with output feedback, such that the uncertain system simultaneously satisfies finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathscr {L}_{2}$ </tex-math></inline-formula> gain in the presence of worst-case exogenous disturbances. The designed min-max controller minimizes an upper bound on the considered performance index, providing a guaranteed cost for disturbance attenuation performance. Finite-time bounded state feedback controller design is shown to be a special case of the proposed method. The performance efficacy and applicability of the controller designed using the proposed iterative algorithm are compared with some of the recent methods from the literature.

A Minimax Framework for Two-Agent Scheduling With Inertial Constraints

Autonomous agents are promising in applications such as intelligent transportation and smart manufacturing, and scheduling of agents has to take their inertial constraints into consideration. Most current researches require the obedience of all agents, which is hard to achieve in non-dedicated systems such as traffic intersections. In this article, we establish a minimax framework for the scheduling of two inertially constrained agents with no cooperation assumptions. Specifically, we first provide a unified and sufficient representation for various types of situation information, and define a state value function characterizing the agent's preference of states under a given situation. Then, the minimax control policy along with the calculation methods is proposed which optimizes the worst-case state value function at each step, and the safety guarantee of the policy is also presented. Furthermore, several generalizations are introduced on the applicable scenarios of the proposed framework. Numerical simulations show that the minimax control policy can reduce the largest scheduling cost by $13.4\%$ compared with queueing and following policies. Finally, the effects of decision period, observation period and inertial constraints are also numerically discussed.

Design Optimization of a Gas Turbine Engine for Marine Applications: Off-Design Performance and Control System Considerations.

This paper addresses a design optimization of a gas turbine (GT) for marine applications. A gain-scheduling method incorporating a meta-heuristic optimization is proposed to optimize a thermodynamics-based model of a small GT engine. A comprehensive control system consisting of a proportional integral (PI) controller with additional proportional gains, gain scheduling, and a min-max controller is developed. The modeling of gains as a function of plant variables is presented. Meta-heuristic optimizations, namely a genetic algorithm (GA) and a whale optimization algorithm (WOA), are applied to optimize the designed control system. The results show that the WOA has better performance than that of the GA, where the WOA exhibits the minimum fitness value. Compared to the unoptimized gain, the time to reach the target of the power lever angle is significantly reduced. Optimal gain scheduling shows a stable response compared with a fixed gain, which can have oscillation effects as a controller responds. An effect of using bioethanol as a fuel has been observed. It shows that for the same input parameters of the GT dynamics model, the fuel flow increases significantly, as compared with diesel fuel, because of its low bioethanol heating value. Thus, a significant increase occurs only at the gain that depends on the fuel flow.

ADP-Based Remote Secure Control for Networked Control Systems Under Unknown Nonlinear Attacks in Sensors and Actuators

In this article, we concentrate on a class of networked control systems (NCSs) under the unknown nonlinear attacks, which target the sensors and actuators with remote communication channels. To attenuate the attacks remotely, the remote secure control scheme based on the adaptive dynamic programming (ADP) is proposed. First, the dynamic process of NCSs with nonlinear sensors and actuators attacks is analyzed and an adaptive remote estimator is designed to obtain the state information of the NCSs from a long distance, which is the key to achieve the purpose of remote control. Moreover, to compensate for the unknown nonlinear attacks, the adaptive law of the remote estimator is presented based on recursive least square. Furthermore, we consider the influence of the estimation errors, the minimax control theory is applied to improve the design of the policy iteration algorithm, and the ADP-based remote secure control strategy is proposed to rely on the remote estimation information. Then, the neural networks are built to implement the online algorithm. Finally, results’ analysis illustrates on two networked power systems the effectiveness of the proposed method.

Chaotic synchronization of neuronet-type stochastic complex networks using decentralized differential minimax controllers

ABSTRACT Based on differential minimax control, this paper develops a novel theoretic design to achieve chaotic synchronization of neuronet-type stochastic complex networks that are heavily influenced by noise signals. According to robust inverse optimality, the proposed method is mathematically formulated by using stochastic Lyapunov technique and the associated Hamilton-Jacobi-Isaacs (HJI) equation, which ensures that the system accomplishes the best rational synchronization in probability, meanwhile, to reduce noises to a predefined level with stability margins. To verify analytical results, a numerical example is given to show the effectiveness of the proposed technique.

Robust Stackelberg Differential Game With Model Uncertainty

This article formalizes two types of modeling uncertainties in a stochastic Stackelberg linear-quadratic (LQ) differential game and then discusses the associated robust Stackelberg strategy design for either the leader or follower. Both uncertainties are primarily motivated by practical applications in engineering and management. The first uncertainty is connected to a disturbance unknown to the follower but known to the leader. A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">soft-constraint</i> min-max control is applied by the follower to determine the optimal response, and then an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">augmented</i> LQ forward-backward stochastic differential equation control is solved by the leader to ensure a robust strategy design. The second uncertainty involves a disturbance, the realization of which can be completely observed by the follower, but only its distribution can be accessed by the leader. Thus, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hard-constraint</i> min-max control on an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">affine-equality-constraint</i> is studied by the leader to address the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exact-optimal</i> robust design. Moreover, based on a weak convergence technique, a minimizing sequence of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">near-optimal</i> robust designs is constructed, which is more tractable in computation. Some numerical results of the abovementioned robust strategies are also presented.

Advanced Control Algorithm for FADEC Systems in the Next Generation of Turbofan Engines to Minimize Emission Levels

New propulsion systems in aircrafts must meet strict regulations and emission limitations. The Flightpath 2050 goals set by the Advisory Council for Aviation Research and Innovation in Europe (ACARE) include reductions of 75%, 90%, and 65% in CO2, NOx, and noise, respectively. These goals are not fully satisfied by marginal improvements in gas turbine technology or aircraft design. A novel control design procedure for the next generation of turbofan engines is proposed in this paper to improve Full Authority Digital Engine Control (FADEC) systems and reduce the emission levels to meet the Flightpath 2050 regulations. Hence, an Adaptive Network–based Fuzzy Inference System (ANFIS), nonlinear autoregressive network with exogenous inputs (NARX) techniques, and the block-structure Hammerstein–Wiener approach are used to develop a model for a turbofan engine. The Min–Max control structure is chosen as the most widely used practical control algorithm for gas turbine aero engines. The objective function is considered to minimize the emission level for the engine in a pre-defined maneuver while keeping the engine performance in different aspects. The Genetic Algorithm (GA) is applied to find the optimized control structure. The results confirm the effectiveness of the proposed approach in emission reduction for the next generation of turbofan engines.

Min-max Control for Vibration Suppression of Mobile Manipulator with Active Suspension System

Min-max Control for Vibration Suppression of Mobile Manipulator with Active Suspension System

Compressor Degradation Management Strategies for Gas Turbine Aero-Engine Controller Design

The Advisory Council for Aeronautics Research in Europe (ACARE) Flight Path 2050 focuses on ambitious and severe targets for the next generation of air travel systems (e.g., 75% reduction in CO2 emissions per passenger kilometre, a 90% reduction in NOx emissions, and a 65% reduction in the noise emissions of flying aircraft relative to the capabilities of typical new aircraft in 2000). Degradation is an inevitable phenomenon as aero-engines age with significant impacts on the engine performance, emissions level, and fuel consumption. The engine control system is a key element capable of coping with degradation consequences subject to the implementation of an advanced management strategy. This paper demonstrates a methodological approach for aero-engine controller adjustment to deal with degradation implications, such as emission levels and increased fuel consumption. For this purpose, a component level model for an aero-engine was first built and transformed to a block-structured Wiener model using a system identification approach. An industrial Min-Max control strategy was then developed to satisfy the steady state and transient limit protection requirements simultaneously while satisfying the physical limitation control modes, such as over-speed, surge, and over-temperature. Next, the effects of degradation on the engine performance and associated changes to the controller were analysed thoroughly to propose practical degradation management strategies based on a comprehensive scientometric analysis of the topic. The simulation results show that the proposed strategy was effective in restoring the degraded engine performance to the level of the clean engine while protecting the engine from physical limitations. The proposed adjustments in the control strategy reduced the fuel consumption and, as a result, the emission level and carbon footprint of the engine.

Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory

In this paper, we study the quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory. A global well-posedness theorem regarding the solutions to its Cauchy problem is given. We formulate the minimax control problem with bilinear control inputs and corresponding disturbances. Under some assumptions, we prove the existence of optimal pairs and give necessary optimality conditions for optimal pairs in some observation cases.

Nonlinear generalized predictive controller based on ensemble of NARX models for industrial gas turbine engine

New design and operation of modern gas turbine engines (GTEs) are becoming more and more complex where several limitations and control modes should be fulfilled at the same time to accomplish a safe and ideal performance for the engine. For this purpose, a constrained multi-input multi-output (MIMO) non-linear model predictive controller (NMPC) based on neural network model is designed to fulfill the control requirements of a Siemens SGT-A65 three-spool aero-derivative gas turbine engine (ADGTE) used for power generation. However, the implementation of NMPC in real time has two challenges: Firstly, the design of an accurate non-linear model, which can run many times faster than real time. Secondly, the usage of a rapid and reliable optimization algorithm to solve the optimization problem in real time. To solve these issues, the constrained MIMO NMPC is created based on the generalized predictive control (GPC) algorithm as a result of its clarity, ease of use, and capacity to deal with problems in one algorithm. In addition, seven ensembles of eight multi-input single-output (MISO) non-linear autoregressive network with exogenous inputs (NARX) models are used as a base model for the GPC controller to predict the future process outputs. Estimation of free and forced responses of the GPC based on the neural network (NN) model of the plant each sampling time without performing instantaneous linearization is proposed in this study, which reduces the NMPC optimization problem to a linear optimization problem at each sampling step. In addition, the Hildreth's quadratic programming algorithm is used to solve the quadratic optimization problem within the NMPC controller, which offers ease of use and reliability in real time applications. To demonstrate the performance of the NNGPC controller developed in this study, we have compared the performance of the neural network generalized predictive control (NNGPC) controller to the existing controller of the SGT-A65 engine. The simulation results show that the NNGPC has demonstrated output responses with less oscillatory behavior and smoother control actions to the sudden variation in the electric load disturbance than those observed in the existing min-max controller. However, the min-max controller has faster response than that of the NNGPC controller.