非线性模型预测控制理论及应用研究
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摘要
本文沿着理论研究与工程实际相结合的设计思路，较为系统和全面的研究了非线性模型预测控制理论，提出改进新算法；探讨了非线性模型预测控制理论在自主水下航行器控制系统设计中的应用，丰富和发展了模型预测控制理论，本论文的主要工作及意义有以下几个方面：
1) 从工程应用的角度研究有限域无终端约束广义预测控制稳定性充分条件，为有约束广义预测控制稳定性研究奠定了基础。提出充分利用预测信息的广义预测控制算法和基于Smith预估器的自适应广义预测控制算法，改善闭环系统过渡品质。
2) 提出并研究约束统一数学表达式。研究有限域约束广义预测控制稳定性充分条件。深入分析约束预测控制在线优化算法、初始可行解问题和约束不可行时的处理方案。提出改进系统性能的超调约束广义预测控制算法，研究遗传算法在非二次型性能指标约束广义预测控制中的应用。
3) 研究神经网络非线性递推多步预测模型及非递推多步预测模型，并构造基于三层静态前向神经网络的预测模型。研究基于线性参数神经网络的预测控制和基于非线性参数神经网络的预测控制，分析神经网络广义预测控制系统结构，推导神经网络递推预测模型灵敏度导数。在Newton-Rhapson广义预测控制算法及梯度下降法次优广义预测控制算法的基础上，提出采用多层前向神经网络改进在线学习算法的自适应BP神经网络广义预测控制算法和基于RBF神经网络的非线性广义预测控制算法。研究神经网络作为优化器优化模型预测控制性能指标的模型预测神经网络控制。
4) 研究基于微分几何方法的反馈线性化技术在非线性模型预测控制中的应用。提出递推QP算法求解二次型性能目标非线性约束MPC优化问题。分析基于反馈线性化的MPC稳定性。提出基于仿射神经网络模型的约束非线性模型预测控制。研究非仿射非线性系统反馈线性化方法——逆系统方法，及其在非线性模型预测控制中的应用。
5) 研究非线性模型预测控制分解协调算法，分析大系统目标协调算法在模型预测控制中的应用。提出基于大系统空间分解和时间分解的非线性预测控制在线优化三级分解协调算法。
6) 基于6自由度水下航行器通用动力学模型，建立自主式水下航行器波动
西北工业大学博士学位论文
运动方程。研究浅水环境中波浪对水下航行器位置保持的影响，并建立波浪干
扰模型。应用模型预测控制，解决水下航行器有波浪干扰环境下的位置保持问
题。
Nonlinear Model based predictive control (NMPC) not only is a valuable approach for solving practical control problems, but also is the frontier of Nonlinear control theory. The perceptible successes of MPC strategies can be attributed to several factors including its inherent ability to handle input and output constraints, time delay and incorporation of an explicit model of the plant into the optimization problem. This dissertation discusses two kinds of nonlinearity (or nonlinear system). One is a special nonlinear system with constraints, a linear system with time delay, and the affine-type nonlinear system, and the other one is a general nonlinear system with constrains.
In the first part, not only a general overview of the linear and nonlinear model based predictive control algorithms is provided, also a generalized predictive control (GPC) algorithm is proposed, which takes full advantage of predictive information. Meanwhile, an adaptive Smith-generalized predictive controller is used to improve the dynamic behavior of the time-delay system. The Smith predictor structure instead of an optimal predictor in GPC is used to compute the predictions of the output of the plant and to compute the sequence of future control signal. Based on the model matching on the frequency of zero, the system parameters and delay time are identified by RFFM(Recursive Forgetting Factor Method) or RHT(Recursive Householder Transform). The algorithm can be applied to the control of the long time delay system with variable parameters and with unknown delay time.
In the second part, the predictive control algorithms with constraints of variables are derived. The stability of the closed loop predictive control system and optimization feasibility are investigated. Some technical solutions to the optimization unfeasibility are proposed. Genetic algorithm (GA) is used for optimizing predictive controllers. GAs allow the use of Non-quadratic index so that it improves control performance.
In the third part, since the plant is a general nonlinear model, the neural generalized predictive control algorithms, recursive least squares (RLS) learning algorithm, based on multilayer feedforward neural network, and orthogonal least square (OLS) learning algorithm, based on radial basic neural network, are presented respectively. Meanwhile, the model predictive neural control is investigated, in which the neural network controller is optimized using a calculus of variations approach to minimize the MPC cost function and is differs from work above.
In the fourth part, the development of a nonlinear model predictive control algorithm based on feedback linearization method is studied. Two feedback linearization methods are presented. One is differential geometry method for affine-type nonlinear system, and the other one is based on the inversion of nonlinear system, which is capable of managing general nonlinear system from the theoretical point of view. Unfortunately, the inversion of nonlinear system sometimes is hard to be obtained.
In the fifth part, since the time of computation can confine the applied area of NMPC, a hierarchical predictive control algorithm is developed. This algorithm is based on the decompositon-coordinations method.
In the last part, NMPC studied above are applied to AUV's station keeping in a shallow waterwave environment.
1) 从工程应用的角度研究有限域无终端约束广义预测控制稳定性充分条件，为有约束广义预测控制稳定性研究奠定了基础。提出充分利用预测信息的广义预测控制算法和基于Smith预估器的自适应广义预测控制算法，改善闭环系统过渡品质。
2) 提出并研究约束统一数学表达式。研究有限域约束广义预测控制稳定性充分条件。深入分析约束预测控制在线优化算法、初始可行解问题和约束不可行时的处理方案。提出改进系统性能的超调约束广义预测控制算法，研究遗传算法在非二次型性能指标约束广义预测控制中的应用。
3) 研究神经网络非线性递推多步预测模型及非递推多步预测模型，并构造基于三层静态前向神经网络的预测模型。研究基于线性参数神经网络的预测控制和基于非线性参数神经网络的预测控制，分析神经网络广义预测控制系统结构，推导神经网络递推预测模型灵敏度导数。在Newton-Rhapson广义预测控制算法及梯度下降法次优广义预测控制算法的基础上，提出采用多层前向神经网络改进在线学习算法的自适应BP神经网络广义预测控制算法和基于RBF神经网络的非线性广义预测控制算法。研究神经网络作为优化器优化模型预测控制性能指标的模型预测神经网络控制。
4) 研究基于微分几何方法的反馈线性化技术在非线性模型预测控制中的应用。提出递推QP算法求解二次型性能目标非线性约束MPC优化问题。分析基于反馈线性化的MPC稳定性。提出基于仿射神经网络模型的约束非线性模型预测控制。研究非仿射非线性系统反馈线性化方法——逆系统方法，及其在非线性模型预测控制中的应用。
5) 研究非线性模型预测控制分解协调算法，分析大系统目标协调算法在模型预测控制中的应用。提出基于大系统空间分解和时间分解的非线性预测控制在线优化三级分解协调算法。
6) 基于6自由度水下航行器通用动力学模型，建立自主式水下航行器波动
西北工业大学博士学位论文
运动方程。研究浅水环境中波浪对水下航行器位置保持的影响，并建立波浪干
扰模型。应用模型预测控制，解决水下航行器有波浪干扰环境下的位置保持问
题。
Nonlinear Model based predictive control (NMPC) not only is a valuable approach for solving practical control problems, but also is the frontier of Nonlinear control theory. The perceptible successes of MPC strategies can be attributed to several factors including its inherent ability to handle input and output constraints, time delay and incorporation of an explicit model of the plant into the optimization problem. This dissertation discusses two kinds of nonlinearity (or nonlinear system). One is a special nonlinear system with constraints, a linear system with time delay, and the affine-type nonlinear system, and the other one is a general nonlinear system with constrains.
In the first part, not only a general overview of the linear and nonlinear model based predictive control algorithms is provided, also a generalized predictive control (GPC) algorithm is proposed, which takes full advantage of predictive information. Meanwhile, an adaptive Smith-generalized predictive controller is used to improve the dynamic behavior of the time-delay system. The Smith predictor structure instead of an optimal predictor in GPC is used to compute the predictions of the output of the plant and to compute the sequence of future control signal. Based on the model matching on the frequency of zero, the system parameters and delay time are identified by RFFM(Recursive Forgetting Factor Method) or RHT(Recursive Householder Transform). The algorithm can be applied to the control of the long time delay system with variable parameters and with unknown delay time.
In the second part, the predictive control algorithms with constraints of variables are derived. The stability of the closed loop predictive control system and optimization feasibility are investigated. Some technical solutions to the optimization unfeasibility are proposed. Genetic algorithm (GA) is used for optimizing predictive controllers. GAs allow the use of Non-quadratic index so that it improves control performance.
In the third part, since the plant is a general nonlinear model, the neural generalized predictive control algorithms, recursive least squares (RLS) learning algorithm, based on multilayer feedforward neural network, and orthogonal least square (OLS) learning algorithm, based on radial basic neural network, are presented respectively. Meanwhile, the model predictive neural control is investigated, in which the neural network controller is optimized using a calculus of variations approach to minimize the MPC cost function and is differs from work above.
In the fourth part, the development of a nonlinear model predictive control algorithm based on feedback linearization method is studied. Two feedback linearization methods are presented. One is differential geometry method for affine-type nonlinear system, and the other one is based on the inversion of nonlinear system, which is capable of managing general nonlinear system from the theoretical point of view. Unfortunately, the inversion of nonlinear system sometimes is hard to be obtained.
In the fifth part, since the time of computation can confine the applied area of NMPC, a hierarchical predictive control algorithm is developed. This algorithm is based on the decompositon-coordinations method.
In the last part, NMPC studied above are applied to AUV's station keeping in a shallow waterwave environment.
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