Feedback stabilization of linear time-invariant (LTI) and single-input single-output (SISO) plants is considered within the framework of two-degree-of-freedom (2DOF) compensators, using only stable compensator components. In the classical 1DOF (or single feedback loop) setting, it is well known that a given plant can be stabilized by a stable controller if and only if it satisfies the parity interlacing property (PIP). With the 2DOF architecture proposed here, using stable components only, stabilization is possible for all plants with proper rational transfer functions. Our strategy is to create an effective plant that is biproper and has all its zeros in the left half-plane (LHP). Subsequently, a single large enough scalar gain (either positive or negative) is guaranteed to stabilize the system. We present several examples, including a cart with a double pendulum. While successful stabilization is mathematically achieved with stable compensator components in each case, some systems require high final gains.
In this paper, we present a novel formulation involving a coupled ODE-PDE system with memory effects. The system dynamics are modeled using PDEs for heat distribution and ODEs for discrete system states, with an emphasis on incorporating memory terms that influence system behavior over time. A state feedback control law is designed to stabilize the system using the backstepping approach globally. The well-posedness of the closed-loop system is established through rigorous mathematical proofs, ensuring the existence and uniqueness of solutions. Exponential stability is demonstrated using a new Lyapunov function and an analysis of energy decay rates. The article concludes with a numerical example that validates the theoretical findings, showcasing the convergence of system states to equilibrium and confirming the effectiveness of the proposed control strategy.
This paper presents an event-triggered model predictive control (ET-MPC) strategy for a DC-DC buck converter to reduce computational burden while maintaining high dynamic performance. A four-mode discrete-time model is established to accurately capture the converter switching behavior, and a Kalman filter is integrated into the control framework to estimate load disturbances and improve control accuracy. Unlike conventional time-triggered MPC (TT-MPC), which solves an optimization problem at every time-step, the proposed ET-MPC evaluates the optimal switching sequence only when a voltage deviation exceeds a predefined threshold. This mechanism significantly reduces the number of online optimizations while preserving the regulation of output voltage. Simulation results demonstrate that ET-MPC achieves up to 94% reduction in computational effort with comparable transient response, low steady-state error, and acceptable switching frequency. The proposed controller enables an efficient real-time implementation of model predictive control (MPC) for power converters under varying operating conditions.
Wing-assisted inclined running (WAIR), an impressive evolutionary capability observed in young Chukar birds, is an attractive maneuver that can be extended to legged aerial systems like Husky, a multimodal aerial-legged robot. This study proposes a control method using a single rigid body (SRB) model with massless legs and thruster forces collocated at the center of mass of the rigid body. A model predictive controller (MPC) is then used to find the optimal ground reaction forces, thruster forces, and moments to track a reference position and velocity trajectory. An analysis on the controllability of the linearized dynamics also shows the effect of thrusters on a legged robot. matlab simulation results of a high-fidelity model on a slope of 40 deg are obtained that highlight the fact that posture manipulation can be used to vector thrust forces on steep slopes. The simulation also provides insight into how the combined efforts of the thrusters and the tractive forces from the legs make WAIR possible in thruster-assisted legged systems.
Demand response has become an important part of smart home energy management, and an excellent demand response policy can be very effective in reducing energy consumption and comfort violation. However, the uncertainty of renewable energy, the complex interaction between photovoltaic (PV) systems, controllable equipment and the grid, and the uncertain behavior of users bring great challenges to the optimization of smart home energy management. In this paper, we propose an intelligent home energy management framework, dual predictive control-deep deterministic policy gradient method for smart home energy management systems (D2PG-SHEMS). Our method employs an ensemble model combining random forest (RF) and long short-term memory (LSTM) networks, where deep Q-network (DQN) is employed to optimize the ensemble parameters for accurate PV power forecasting. Based on the ensemble model's predictions, the control module utilizes deep deterministic policy gradient (DDPG) combined with imitation learning (IL) to enhance training efficiency for optimal energy management. According to the experimental results over a 72-h testing period, the proposed method reduces energy costs by 69.7% and 34.6% compared to the rule based control (RBC)-based and standard RL methods, respectively, while maintaining the comfort violation level at 35.190.
