Abstract This paper investigates household energy management systems that integrate renewable energy sources and battery storage, modeled as discrete-time optimization problems. Motivated by global trends toward decarbonization and recent policy initiatives promoting distributed energy resources, a data-driven method is proposed that combines fuzzy-rule networks with reinforcement learning in an actor-critic architecture. The controller adaptively regulates power demand while treating renewable energy as an uncertain disturbance. Relying only on real-time demand and battery status data, it aims to minimize electricity costs and preserve battery health. Validation addresses uncertainties in energy prices, user behavior, and environmental conditions. A virtual desired state of charge enhances operational stability, and comparative results confirm the controller’s effectiveness in reducing costs and optimizing battery performance.

The problem of discontinuous derivatives with respect to the control effort is observed in the prototype of preproduction DC motor torque-control. This behavior violates the basic requirement of conventional adaptive controllers. To overcome this issue, a quantum-inference fuzzy rules emulated network (QFREN) is developed, enabling the crossing state of discontinuity through a coherent superposition of its qbit membership functions. The adjustable parameters, which encompass both the linear parameters of QFREN and the nonlinear parameters of the rotation gate and quantum-controlled gate, are adjusted using the derived learning laws. Moreover, theoretical results are provided to ensure the convergence of the tracking error based on the selection of the designed variables in a practical context. Experimental validation is conducted to verify the effectiveness of the proposed controller. Additionally, comparative results with similar schemes are presented to highlight the advantages of the proposed approach. Note to Practitioners—The presence of discontinuous derivatives and nonlinearities, such as dead-zone, can compromise the closed-loop performance of control systems. Utilizing adaptive controllers based on quantum computation and neural networks (QNN) appears promising in mitigating these challenges. However, QNN approaches have predominantly remained in theoretical and numerical simulation contexts. In this work, an application of QFREN as a controller is introduced in a practical control engineering scenario. QFREN demonstrates its effectiveness in addressing the issue of discontinuous derivatives and compensating for unknown nonlinearities.

This article presents a novel adaptive control approach for a class of unknown discrete-time systems using piecewise derivatives derived from experimentally obtained input-output characteristics of the controlled plant. The control law is formulated using a multi-input fuzzy rules emulated network (MiFREN). The learning law is developed to address the issue of catastrophic forgetting, in alignment with the proposed information matrix. Closed-loop analysis demonstrates convergence of the tracking error and weight parameters under feasible conditions. Validation through experiments with a DC-motor torque control system, alongside comparative controllers, demonstrates the superior tracking performance of the proposed method and its effective mitigation of forgetting during tracking tasks.

This article proposes an optimal controller based on reinforcement learning (RL) for a class of unknown discrete-time systems with non-Gaussian distribution of sampling intervals. The critic and actor networks are implemented using the MiFRENc and MiFRENa architectures, respectively. The learning algorithm is developed with learning rates determined through convergence analysis of internal signals and tracking errors. Experimental systems with a comparative controller are conducted to validate the proposed scheme, and comparative results show superior performance for non-Gaussian distributions, with weight transfer for the critic network omitted. Additionally, the proposed learning laws, using the estimated co-state, significantly improve dead-zone compensation and nonlinear variation.

In this work, the affine equivalent model (AEM) is developed by using only the controlled systems's input-output data and it's relation based on fuzzy rules. Multi-input fuzzy rules emulated network (MiFREN) is used as function approximator when learning laws are designed to reduce the model error. Furthermore, AEM stability is guaranteed according to Lyapunov by theorem III.1. Thereafter, the control law is proposed with the information obtained by AEM. The tracking error resulted from the closed-loop system is proved as a convergent sequence by Lemma IV.1. The main advantage results in a simple control scheme and low computational cost. Numerical discrete-time systems (linear and nonlinear) are used to validate the performance of the proposed scheme altogether with the comparison results.

A kinematic redundancy robot is considered as a class of unknown nonlinear discrete-time systems. The compact form dynamic linearization is firstly utilized to establish the equivalent model of the robotic system. Thereafter, the adaptive controller is derived by fuzzy rules emulated network while the learning law is designed to minimize both the tracking error and the control effort energy with the stability analysis. The experimental system is constructed to validate the performance of closed-loop systems.

An adaptive controller for regulating and dimming problems of LED current control is developed in this article when the LED driving system is considered as a class of unknown nonlinear discrete-time systems. The controller is designed by a Fuzzy-rules emulated network (FREN) with direct human knowledge as IF-THEN rules of the controlled plant. The online learning algorithm is established to tune all adjustable parameters of FREN with the convergence analysis. The prototyping system is constructed by using Raspberry Pi model B as a main processing unit. Experimental results validate the satisfied performance for both current regulation and dimmer applications with positive and negative slopes.

A direct adaptive controller based on fuzzy rules emulated network (FREN) for a class of unknown nonlinear discrete-time systems is addressed in this article. According to the fuzzy inference system inside FREN, the human knowledge about the unknown systems is transferred to be if–then rules for setting the network structure. All adjustable parameters are tuned by the on-line learning mechanism with time varying learning rate. This variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the convergence of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The theoretical validation is delineated by the experimental setup with the commercial omni-directional mobile robot system.

A direct adaptive control system for a class of unknown nonaffine discrete-time plants is introduced in this article. The proposed control law is constructed by the estimated system linearization with adjustable networks called muti-input fuzzy rules emulated networks or MIFRENs. Only on-line learning phase, the bounded parameters inside MIFRENs and the boundary of control error are given by the proposed theorem. The validation of the main theorem is demonstrated by computer simulation system.

The adaptive controller for a class of nonlinear discrete-time systems based on Multi-Input Fuzzy Rules Emulated Network (MIFREN) is introduced in this article. MIFREN is assigned to identify the unknown plant under control, then a novel control law is introduced based the previously identified plant with another MIFREN. All control parameters, including the learning rates are selected to guarantee bounded close-loop signals, via Lyapunov stability criteria. The performance of the proposed control algorithm is demonstrated by computer simulation results.

This paper proposes an adaptive network architecture, which can emulate the human knowledge as the fuzzy logic rule, and its applications as the controller for nonlinear systems. The structure of this proposed network, multi-input Fuzzy Rule Emulated Network or FREN, is derived based on human knowledge in the form of fuzzy IF-THEN rules. The initial setting of its parameters can be intuitively chosen from expert's experience. During the learning phase based on the gradient search, the learning rate can be adapted itself to remain the stability with the Lyapunov method. The performance of our network is presented by using this network as controller for the single invert pendulum plant and the water bath temperature control system. The comparison results with other conventional control algorithms such as artificial neural networks and PID controllers can be illustrated in each example.

This paper presents a parallel adaptive networks controller which is implemented by our Fuzzy Input Adaptive Network (FIAN). The FIAN is easy to be set initial parameters and structure by the human sense. All FIAN parameters can be adjusted by gradient descent based on Lyapunov stability synthesis during the operation of networks. The gradient adaptive is applied via linear plant parameters approximation at the chain rule of gradient search, The performance of FIAN as controller can be shown by its application which is the controllers for nonlinear plants. Due to our experiments "water bath temperature control system" and "single inverted pendulum" are selected to test the system performance.