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The design and structure of generalized predictive control (GPC) are not simple and intuitive. The performance analysis does not deeply analyze how the controller parameters affect the system characteristics and the relationship between the tracking error caused by the noise and the selected controller parameters. This paper proposes a generalized predictive control, and its design is simple and intuitive for unnecessary solving the Diophantine equation. Then the relationship between desired output, disturbance, and system output is analyzed by the characteristic equation and steady-state analysis. Based on this, the study presents research findings on the steady state of the system and verifies them through simulations. Furthermore, this paper introduces GPC with disturbance compensation and incremental generalized minimum variance control (IGMVC) with disturbance compensation. The conditions for the elimination of disturbance are presented in theory and simulation for the first time.

Based on equivalent-dynamic-linearization model (EDLM), we propose a kind of model predictive control (MPC) for single-input and single-output (SISO) nonlinear or linear systems. After compensating the EDLM with disturbance for multiple-input and multiple-output nonlinear or linear systems, the MPC compensated with disturbance is proposed to address the disturbance rejection problem. The system performance analysis results are much clear compared with the system stability analyses on MPC in current works. And this may help the engineers understand how to design, analyze and apply the controller in practical.

In this paper, we restudy how to modify the model-free adaptive control (MFAC) to reject the disturbance both in single-input single-output (SISO) systems and multiple-input multiple-output (MIMO) systems, with the aim to pave the way for the development of this interesting controller in the future. First of all, in order to accurately describe the nonlinear system model at each time, we compensate the equivalent dynamic linearization model (EDLM) with disturbance and prove it through the definition of differentiability and the Taylor series. Then based on modified EDLM, we redesign MFAC compensated with disturbance and firstly reanalyze the discrete-time nonlinear system through the closed-loop system equation at each time. This is all possible because some nonlinear system functions can be accurately described by the EDLM compensated with disturbance according to Taylor series. At last, several examples are given to verify the theorem.

In this brief, a model-free adaptive predictive control (MFAPC) is proposed. It outperforms the current model-free adaptive control (MFAC) for not only solving the time delay problem in multiple-input multiple-output (MIMO) systems but also relaxing the current rigorous assumptions for sake of a wider applicable range. The most attractive merit of the proposed controller is that the controller design, performance analysis and applications are easy for engineers to realize. Furthermore, the problem of how to choose the matrix {\lambda} is finished by analyzing the function of the closed-loop poles rather than the previous contraction mapping method. Additionally, in view of the nonlinear modeling capability and adaptability of neural networks (NNs), we combine these two classes of algorithms together. The feasibility and several interesting results of the proposed method are shown in simulations.

The model-free adaptive control (MFAC) law is a promising method in applications. We analyzed model-free adaptive control (MFAC) law through closed-loop function to widen its application range., Comment: arXiv admin note: text overlap with arXiv:2009.04248

In this brief, the current robust numerical solution to the inverse kinematics based on Levenberg-Marquardt (LM) method is reanalyzed through control theory instead of numerical method. Compared to current works, the robustness of computation and convergence performance of computational error are analyzed much more clearly by analyzing the control performance of the corrected model free adaptive control (MFAC). Then mainly motivated by minimizing the predictive tracking error, this study suggests a new method of model free adaptive predictive control (MFAPC) to solve the inverse kinematics problem. At last, we apply the MFAPC as a controller for the robotic kinematic control problem in simulation. It not only shows an excellent control performance but also efficiently acquires the solution to inverse kinematic.

We analyzed model-free adaptive control (MFAC) law through closed-loop function to widen its application range., Comment: arXiv admin note: text overlap with arXiv:2008.10164

Current model-free adaptive control (MFAC) method has no been analysed in linear system and is not straightforward for the practical engineers to understand accurately. This correspondence presents a family of MFAC based on a modified equivalent-dynamic-linearization model (EDLM), which facilitates to show the working principle of method more directly and objectively. Compared to the current work, i) the researches on MFAC focus on linear model, which is easy to understand its working behaviour; ii) the full-form EDLM is extended with unmeasured stochastic and measured disturbance, respectively. Then the controllers is modified correspondingly; iii) the stability analysis of system cannot be proved by current contraction mapping technique when the sign of leading coefficient of control input changes, therefore we prove it by analysing the function of the closed-loop poles. Several simulated examples are used to show the principles of this kind of method.

The current model-free adaptive control (MFAC) method is designed on the basis of the equivalent-dynamic-linearization model (EDLM) with neglect of the time delay and disturbance in practical. By comparisons with the current works about MFAC, i) a class of self-tuning controller is proposed based a new EDLM modified by the introduction of time delay and disturbance so as to reflect the real system more objectively. Thereafter, we classify the proposed controller into four cases to enable easier applications; ii) the controller design and stability analysis of system are achievable by analyzing the function of the closed-loop poles. In addition, the issue of how to choose the parameter \lambda in current MFAC by quantity is firstly finished by the analysis of zeros-poles placement and static error of system, whereas this can hardly be realized by the previous contraction mapping method; iii) the study on the proposed method is focused on linear model for easily mastering its working behavior; At last, two examples are used to demonstrate the effectiveness of the proposed method and to point out the deficiencies in the current MFAC theory.

Current model-free adaptive control (MFAC) can hardly deal with the time delay problem in multiple-input multiple-output (MIMO) systems. To solve this problem, a novel model-free adaptive predictive control (MFAPC) method is proposed. Compared to the current MFAC, i) the proposed method is based on a kind of prediction model which derives from the equivalent-dynamic-linearization model (EDLM); ii) the previous assumptions are relaxed and the application range of MFAPC are extended. The leading coefficient of the control input vector in system description is no more restricted to the diagonally dominant square matrix and the permissible ranges of pseudo orders Ly and Lu are extended; iii) the performance analysis and the issue of how to choose the matrix {\lambda} are completed by an easy manner of analyzing the function of the closed-loop poles, however, both problems may not be realized by the previous contraction mapping method.

This correspondence proposes a kind of model-free adaptive control (MFAC) on the basis of full-form equivalent-dynamic-linearization model (EDLM) for the multivariable nonlinear system. Compared with the current MFAC, i) this control law does not have denominator, which is stemmed from the norm of the inverse matrix and it inevitably misses the coupling relationships among the inputs and outputs (I/O) of systems. ii) the current restrictive assumption of a diagonally dominant matrix is reduced to extend its application. iii) the MFAC based on full-form EDLM is more general than the current MFAC based on partial-form and compact-form EDLM. At last, the convergence of tracking error and the BIBO stability of controlled system have been proved, which is one of the open questions in MFAC.

In this paper, a novel partial form dynamic linearization (PFDL) data-driven model-free adaptive predictive control (MFAPC) method is proposed for a class of discrete-time single-input single-output nonlinear systems. The main contributions of this paper are that we combine the concept of MPC with MFAC together to propose a novel MFAPC method. We prove the bounded-input bounded-output stability and tracking error monotonic convergence of the proposed method; Moreover, we discuss the possible relationship between the current PFDL-MFAC and the proposed PFDL-MFAPC. The simulation and experiment are carried out to verify the effectiveness of the proposed MFAPC., Comment: 8 pages,3 figures. arXiv admin note: substantial text overlap with arXiv:1910.08321

In this paper, a novel full form dynamic linearization (FFDL) data-driven model-free adaptive predictive control (MFAPC) method is proposed for a class of discrete-time single-input single-output nonlinear systems. The novelty of MFAPC is that preliminary physical model and the Lyapunov stability theory are not required for the controller design and theoretical analysis. Instead, the proposed MFAPC only uses a new dynamic linearization method called pseudo-gradient (PG) vector, which is merely related to the input/output (I/O) measurement data. The main contributions of this paper are: First, a novel MFAPC with adjustable parameters is proposed; Second, we have proved the bounded-input bounded-output stability, the monotonic convergence of the tracking error, and the internal stability of the proposed method. Third, the proposed MFAPC can be considered as an elegant extension of the current MFAC. The simulations have been carried out to verify the effectiveness of the proposed MFAPC., Comment: 13 pages, 9 figures