Linear Quadratic Optimal Control Theory Research Articles

Optimal Control Strategy of Electro-hydraulic Position Servo System Using Genetic Algorithm

Background: The optimal control strategy has been widely used in electro-hydraulic position servo systems to achieve high-precision position tracking. However, the difficulty of selecting the weighted matrices in optimal control often leads to poor tracking accuracy. Objective: This patent proposes an optimal control strategy using a genetic algorithm to improve the tracking accuracy of the electro-hydraulic servo system. Methods: The patent first established the system state equation of the valve-controlled asymmetric cylinder. Secondly, based on linear quadratic optimal control theory and genetic algorithm, an optimal control strategy using a genetic algorithm was proposed. Finally, the simulation and experimental results showed that the designed controller has high position tracking accuracy . Results: The optimal controller using a genetic algorithm was designed using Matlab/Simulink, and the effectiveness of the controller was verified through simulation. Additionally, experimental results showed that the proposed optimal control controller using a genetic algorithm had higher tracking accuracy than the proportional-integral-derivative controller and traditional backstepping controller for a given reference signal. Conclusion: The control technology of the optimal controller using a genetic algorithm was found to be superior to proportional-integral-derivative and traditional backstepping controllers, and the tracking error of the linear quadratic regulator controller was reported to be relatively small. This demonstrated the effectiveness of the optimal control strategy using a genetic algorithm in this patent.

Optimal Unmanned Ground Vehicle—Unmanned Aerial Vehicle Formation-Maintenance Control for Air-Ground Cooperation

This paper investigates the air–ground cooperative time-varying formation-tracking control problem of a heterogeneous cluster system composed of an unmanned ground vehicle (UGV) and an unmanned aerial vehicle (UAV). Initially, the structure of the UAV–UGV formation-control system is analyzed from the perspective of a cooperative combat system. Next, based on the motion relationship between the UAV–UGV in a relative coordinate system, the relative motion model between them is established, which can clearly reveal the physical meaning of the relative motion process in the UAV–UGV system. Then, under the premise that the control system of the UAG is closed-loop stable, the motion state of the UGV is modeled as an input perturbation. Finally, using a linear quadratic optimal control theory, a UAV–UGV formation-maintenance controller is designed to track the reference trajectory of the UGV based on the UAV–UGV relative motion model. The simulation results demonstrate that the proposed controller can overcome input perturbations, model-constant perturbations, and linearization biases. Moreover, it can achieve fast and stable adjustment and maintenance control of the desired UAV–UGV formation proposed by the cooperative combat mission planning system.

Mean-variance problem for an insurer with dependent risks and stochastic interest rate in a jump-diffusion market

In this paper, we study an optimal investment and reinsurance problem in which the interest rate is driven by the Vasicek process and two dependent classes of insurance business are correlated through a common shock component. The goal of insurer is to find an optimal investment-reinsurance strategy to minimize the variance of terminal net wealth for a given expected terminal net wealth. By using the linear-quadratic optimal control theory and the corresponding Hamilton-Jacobi-Bellman (HJB) equation, the closed-form expressions for the value function and optimal strategies are obtained under the special case of perfect correlation between the bond and stock processes. We present that the solution of the HJB equation is no longer a classical solution, but a viscosity solution due to the non-negativity constraint of the reinsurance strategy. Furthermore, the efficient strategies and efficient frontier are derived explicitly. Finally, we explore some numerical examples to show the influence of model parameters on the optimal investment and reinsurance strategies.

Optimization design of active suspension of vehicle based on LQR control

In this article, we take the 1/4 vehicle model as an example, according to the requirements of the driving performance of vehicles. We establishes the dynamic model of the vehicle, and use the linear quadratic optimal control theory to design the LQG controller of the active suspension, and use MATLAB/simulink to simulate the vehicle dynamic model. The results show that the active suspension with LQG controller has a good effect on the improvement of vehicle running stability and riding comfort.

Research on Maneuvering Trajectory Tracking Accuracy of Target Missile Based on Feedback Linearization

Aiming at the trajectory tracking accuracy of missile target, a trajectory tracking guidance law is designed based on feedback linearization theory and linear quadratic optimal control theory, and the tracking accuracy of the designed trajectory tracking guidance law under different maneuvering trajectories is tested. The motion equations of missiles are typical non-linear motion models, so feedback linearization is introduced as an exact linearization method, and the definition and necessary and sufficient conditions of feedback linearization theory are listed. Firstly, the non-linear equations of the longitudinal motion of target missile are established, and the feedback linearization method is used to linearize the non-linear model accurately. Then, the linearized model is designed by using the linear quadratic optimal control theory, and a target trajectory tracking guidance law is obtained. Finally, given gust disturbance and different maneuvering trajectories, the designed trajectory tracking guidance law is simulated, and the tracking accuracy of the guidance law is studied by changing the control coefficient. The results show that the trajectory tracking guidance law based on feedback linearization has excellent trajectory tracking ability, good tracking accuracy and strong anti-jamming ability under different maneuvering trajectories.

Feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon

This paper deals with the feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon. The optimal control problem of the follower is first studied. Employing the discrete-time linear quadratic (LQ) mean-field stochastic optimal control theory, the sufficient conditions for the solvability of the optimization of the follower are presented and the optimal control is obtained based on the stabilizing solutions of two coupled generalized algebraic Riccati equations (GAREs). Then, the optimization of the leader is transformed into a constrained optimal control problem. Applying the Karush-Kuhn-Tucker (KKT) conditions, the necessary conditions for the existence and uniqueness of the Stackelberg strategies are derived and the Stackelberg strategies are expressed as linear feedback forms involving the state and its mean based on the solutions (Ki,K^i),i=1,2 of a set of cross-coupled stochastic algebraic equations (CSAEs). An iterative algorithm is put forward to calculate efficiently the solutions of the CSAEs. Finally, an example is solved to show the effectiveness of the proposed algorithm.

Simulation and Experimental Study on the Active Stability of High-Speed Trains

An active hunting stability scheme is proposed for the high-speed trains based on frame lateral vibration control. The stability of the vehicle is improved by exerting active control force on the front and rear frames of the bogie. First, a simplified lateral vibration model of a single bogie is established to the control system design. The feedback gain matrix is obtained according to the linear quadratic optimal control theory. Then, the multibody dynamics model of the vehicle is built using SIMPACK, and the linear stability and straight running performance are analyzed under different working configurations. Finally, the active control effects are verified by a scaled roller rig. The results show that this active control scheme to improve the stability performances of vehicles through the feedback of frame vibration state is feasible.

Kalman 1960: The birth of modern system theory

ABSTRACTRudolph E. Kalman is mainly known for the Kalman filter, first published in 1960. In this year, he published two equally important contributions, one about linear state space system theory and the other about linear quadratic optimal control theory. These three domains are intertwined in the later theory of linear quadratic Gaussian control. An extended version of linear quadratic optimal control is put into practice in an example of cooperation in population ecology.

Cooperative Guidance and Collision Avoidance for Multiple Pursuers

This paper presents a cooperative guidance law for an -on- engagement scenario that ensures target interception and collision avoidance between the pursuers along with minimizing their team effort. The guidance law is derived using linear quadratic optimal control theory for a linearized engagement model. The pursuers cooperate with each other to accommodate differences in maneuver capabilities of different team members. A special case of 2-on-2 engagement is also analyzed, for which analytical closed-form formulas for the pursuer’s guidance law are obtained. Various simulation results and experimental validation results, exemplifying the cooperation in different engagements, are also presented.

Time-Coordinated Control for Unmanned Aerial Vehicle Swarm Cooperative Attack on Ground-Moving Target

In this paper, cooperative attack control law analysis and design problems for unmanned aerial vehicle (UAV) swarm attack on ground-moving target with time-coordinated strategies are investigated. First, the time-coordinated control problem for a single UAV is formulated, which is the foundation of solving the problem of a single UAV arriving at the desired attack position relative to ground-moving target at a specific terminal time. Then, relative motion between each UAV and ground-moving target is considered as a finite-time time-varying tracking system problem, and the difference between expected output and system output is defined as tracking error vector. The control law is obtained by linear quadratic optimal control theory to minimize the energy cost in the whole process and the tracking error at the terminal time. Besides, time-coordinated function, which is critical to coordinate terminal time among all UAVs in the UAV swarm, is proposed to model time-coordinated strategies. Finally, numerical simulations show that the proposed control law can steer UAV swarm to arrive at the desired attack positions and achieve the time-coordinated strategies effectively.

Adaptive Optimal Control With Guaranteed Convergence Rate for Continuous-Time Linear Systems With Completely Unknown Dynamics

The traditional linear quadratic optimal control can be summarized as finding the state feedback controller so that the closed-loop system is stable and the performance index is minimum. And, it is well-known that the solution of the linear quadratic optimal control problem can be solved by algebraic Riccati equation. However, the feature of the traditional linear quadratic optimal control theory is that the convergence rate is not specified. This may result in the phenomena of slow convergence. In this paper, we mainly consider the linear quadratic optimal control with guaranteed convergence rate (LQOCGCR) and propose a policy iteration-based adaptive dynamic programming algorithm that includes offline and online versions for finding the solution of the LQOCGCR. Finally, a numerical example is worked out to show the effectiveness of the proposed approach.

Characteristic analysis and optimal control of the thickness and tension system on tandem cold rolling

The tandem cold-rolling process is a multivariable, nonlinear, and strongly coupled complex control procedure, in which the key technologies of automatic gauge control (AGC) and automatic tension control (ATC) are extremely comprehensive, and high precision is required. This paper analyzes the rolling characteristics of tandem cold-rolling process and proposes an innovative multivariable optimization strategy based on inverse linear quadratic (ILQ) optimal control theory for thickness and tension control. First, a new state space model of the tandem cold-rolling process was introduced and verified based on the basic equations of rolling technology and field data. Then, meaningful influence rules on the complex rolling process were obtained by analyzing rolling characteristics. For the complex rolling process, a novel ILQ control strategy was introduced into the thickness and tension control system. As a result, by a series of experiments, the effect of disturbance on the thickness and tension was attenuated to an arbitrary degree of accuracy through the proposed control strategy. Simulation results showed the excellent control performance of the proposed ILQ control strategy compared with the conventional proportion and integration (PI) control strategy.

Assessment of shunted piezoelectric devices for simultaneous noise and vibration reduction: comparison of passive, active and hybrid networks

Structural vibration and noise control of a cavity-backed three-layered smart piezo-coupled rectangular panel system under harmonic or transient loads is achieved by using purely active, passive, and hybrid active/passive piezoelectric shunt networks. Problem formulation is based on the classical lamination plate theory, Maxwell’s equation for piezoelectric materials, linear circuit theory, and wave equation for the enclosed acoustic domain. The orthogonal mode expansions along with the modal coupling theory are employed to obtain the coupled differential equations of the electro-mechanical-acoustic system, which are then put into the convenient state-space form, and subsequently solved numerically in both frequency and time domains. A triple-mode hybrid RLC shunt circuit, in series with an external active voltage source and connected to a single electroded piezoelectric segment, is tuned to the dominant resonance frequencies of the composite structure. The linear quadratic optimal control (LQR) theory is adopted for obtaining the active control gains. The frequency and time domain performances of the passive, active and hybrid multi-modal piezoelectric systems are calculated and discussed in terms of sensor output voltage, local sound pressure, and control effort. It is found that the hybrid control methodology with properly tuned circuit parameters can be an excellent candidate for simultaneous vibration and structure-borne noise control of the cavity-coupled smart panel with decreased control effort. Also, the active control strategy integrated in the hybrid control system is demonstrated to enhance the overall system damping characteristics and improve the control authority at frequencies where the passive shunt network performs weakly. Limiting cases are considered and correctness of the mathematical model is verified by using a commercial finite element software as well as by comparisons with the literature.

Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems

Abstract A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given. Finally, simulation results show the effectiveness of the proposed method.

Infinite horizon linear quadratic Pareto game of the stochastic singular systems

This paper is concerned with the linear quadratic (LQ) Pareto game of the stochastic singular systems in infinite horizon. Firstly, the optimal control problem of the weighted sum cost functional is discussed. Utilizing the equivalent transformation method, the weighted sum LQ optimal control problem is transformed into a stochastic LQ optimization problem. Based on the classical stochastic LQ optimal control theory, the necessary and sufficient condition for the solvability of the indefinite weighted sum LQ optimal control is put forward. Then, the LQ Pareto game of the stochastic singular systems is studied. By the discussion of the convexity of the cost functionals, a sufficient condition for the existence of the Pareto solutions is obtained via the solvability of the corresponding generalized algebraic Riccati equation (GARE). Moreover, we derive all Pareto solutions based on the solution of a Lyapunov equation. Finally, an example is given to show the effectiveness of the proposed results.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

ABSTRACTThis paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

The Research of Discrete Mean - Variance Portfolio Problem with Time-Delay

Due to the financial sector complicated variety of events, each financial problems from changes to know its essence, the change rule, from the change of strategy to formulate relevant policy and policy into effect, etc., the process inevitably has a certain lag. Therefore, in order to better reflect the actual situation, we study the portfolio model with delays in this paper. By joining our delay control item, the optimization model was established, the goal is to maximize earnings expectations. In this paper, it studies the continuous time without delay the mean - variance portfolio problems on the basis of existing research. It established auxiliary problem using the stochastic linear quadratic optimal control theory. Using the maximum principle, the solution of the optimal investment strategy are given and it analysis the case, the conclusion is in conformity with the actual. It studies the existing time delay portfolio strategy problem in discrete time case. Based on the stochastic LQ (linear quadratic) optimal control theory, it established the discrete time model with time delay. The paper has carried on the solution and example analysis.

Optimal control for jitter suppression of clutch engagement in upshift process of electric vehicles

In the shift process of large-order automatic transmission, jitter phenomenon is common in clutch engagement process, which greatly affects the ride comfort of the vehicle. In this article, the jitter dynamic model of clutch engagement process was established with lumped mass method and virtual displacement principle. Specific to clutch engagement stage, the optimal control of the coordination between driving motor and wet clutch was studied. In accordance with the jitter dynamic model, the state–space equation with controlling variables of motor torque and clutch friction torque was established. In this optimization problem, the torsion angle, torsion angular velocity, and shift jerk are selected as optimization targets. Utilizing the linear quadratic optimal control theory, the optimal trajectory of motor torque and clutch friction torque was obtained. Aiming at the dynamic responses in clutch engagement process, the optimal control in different conditions of weight coefficients, initial torsion angles, and resistance torques was studied. Results showed that the optimal control strategy could obviously reduce the jitter; in addition, the weight coefficient should be determined according to actual situation reasonably.

Research on the Vibration Control Algorithms for Large Space Truss Structure Based on Precise Integration Method

In this paper, vibration control algorithms for a large space truss structure are investigated. First, a precise integration method is used to solve the differential equation such that the validity and efficiency of the algorithm are guaranteed. Second, on the basis of the discrete algebraic equation combined with the decentralized control theory, the solving method of the control force based on the linear quadratic (LQ) optimal control theory is improved. Third, a new control method, the eigenvalue control method, is proposed in this paper, and its relationship with the LQ optimal control method is discussed. Finally, these two control methods are applied to the structure to analyze the effectiveness of vibration suppression. The simulation results show that the proposed algorithms can quickly suppress the vibration of a large space truss structure.

OPTIMAL IMPACT ANGLE CONTROL GUIDANCE LAWS AGAINST A MANEUVERING TARGET

Optimal impact angle control guidance law and its variants for intercepting a maneuvering target are introduced in this paper. The linear quadratic(LQ) optimal control theory is reviewed first to setup framework of guidance law derivation, called the sweep method. As an example, the inversely weighted time-to-go energy optimal control problem to obtain the optimal impact angle control guidance law for a fixed target is solved via the sweep method. Since this optimal guidance law is not applicable for a moving target due to the angle mismatch at the impact instant, the law is modified to three different biased proportional navigation(PN) laws: the flight path angle control law, the line-of-sight(LOS) angle control law, and the relative flight path angle control law. Effectiveness of the guidance laws are verified via numerical simulations.