Suboptimal control law for a near-space hypersonic vehicle based on Koopman operator and algebraic Riccati equation

This paper presents a novel suboptimal attitude tracking controller based on the algebraic Riccati equation for a near-space hypersonic vehicle (NSHV). Since the NSHV’s attitude dynamics is complexly nonlinear, it is hard to directly construct an appropriate algebraic Riccati equation. We design the construction based on the Chebyshev series and the Koopman operator theory, which includes three steps. First, the Chebyshev series are considered to transform the error dynamics of the NSHV’s attitude into a polynomial system. Second, the Koopman operator is used to obtain a series of high-dimensional linear dynamics to approximate each of the polynomial system’s vector fields. In this step, our contribution is to determine a well-posed linear dynamics with the minimal dimension to approximate the original nonlinear vector field, which helps to design the control law and analyze the control performance. Third, based on the high-dimensional dynamics, the NSHV’s attitude error dynamics is separated into the linear part and the nonlinear part, such that the algebraic Riccati equation can be constructed according to the linear part. Then, the suboptimal error feedback control law is derived from the algebraic Riccati equation. The closed-loop control system is proved to be locally exponentially stable. Finally, the numerical simulation demonstrates the effectiveness of the suboptimal control law.

Hierarchical Robust Adaptive Control for Wind Turbines with Actuator Fault

This paper solves the problem of regulating the rotor speed tracking error for wind turbines in the full-load region by an effective robust-adaptive control strategy. The developed controller compensates for the uncertainty in the control input effectiveness caused by a pitch actuator fault, unmeasurable wind disturbance, and nonlinearity in the model. Wind turbines have multi-layer structures such that the high-level structure is nonlinearly coupled through an aggregation of the low-level control authorities. Hence, the control design is divided into two stages. First, an ℒ2 controller is designed to attenuate the influence of wind disturbance fluctuations on the rotor speed. Then, in the low-level layer, a controller is designed using a proposed adaptation mechanism to compensate for actuator faults. The theoretical results show that the closed-loop equilibrium point of the regulated rotor speed tracking error dynamics in the high level is finite-gain ℒ2 stable, and the closed-loop error dynamics in the low level is globally asymptotically stable. Simulation results show that the developed controller significantly reduces the root-mean- square of the rotor speed error compared to some well-known works, despite the largely fluctuating wind disturbance, and the time-varying uncertainty in the control input effectiveness.

The Predictive Dynamics of Happiness and Well-Being

We offer an account of mental health and well-being using the predictive processing framework (PPF). According to this framework, the difference between mental health and psychopathology can be located in the goodness of the predictive model as a regulator of action. What is crucial for avoiding the rigid patterns of thinking, feeling and acting associated with psychopathology is the regulation of action based on the valence of affective states. In PPF, valence is modelled as error dynamics—the change in prediction errors over time . Our aim in this paper is to show how error dynamics can account for both momentary happiness and longer term well-being. What will emerge is a new neurocomputational framework for making sense of human flourishing.

Synchronization in Dynamically Coupled Fractional-Order Chaotic Systems: Studying the Effects of Fractional Derivatives

This study presents the effectiveness of dynamic coupling as a synchronization strategy for fractional chaotic systems. Using an auxiliary system as a link between the oscillators, we investigate the onset of synchronization in the coupled systems and we analytically determine the regions where both systems achieve complete synchronization. In the analysis, the integration order is considered as a key parameter affecting the onset of full synchronization, considering the stability conditions for fractional systems. The local stability of the synchronous solution is studied using the linearized error dynamics. Moreover, some statistical metrics such as the average synchronization error and Pearson’s correlation are used to numerically identify the synchronous behavior. Two particular examples are considered, namely, the fractional-order Rössler and Chua systems. By using bifurcation diagrams, it is also shown that the integration order has a strong influence not only on the onset of full synchronization but also on the individual dynamic behavior of the uncoupled systems.

T-S Fuzzy Model-Based Fault Detection for Continuous Stirring Tank Reactor

Continuous stirring tank reactors are widely used in the chemical production process, which is always accompanied by nonlinearity, time delay, and uncertainty. Considering the characteristic of the actual reaction of the continuous stirring tank reactors, the fault detection problem is studied in terms of the T-S fuzzy model. Through a fault detection filter performance analysis, the sufficient condition for the filtering error dynamics is obtained, which meets the exponential stability in the mean square sense and the given performance requirements. The design of the fault detection filter is transformed into one that settles the convex optimization issue of linear matrix inequality. Numerical analysis shows the effectiveness of this scheme.

Trajectory Tracking Control for Underactuated USV with Prescribed Performance and Input Quantization

This paper is devoted to the problem of prescribed performance trajectory tracking control for symmetrical underactuated unmanned surface vessels (USVs) in the presence of model uncertainties and input quantization. By combining backstepping filter mechanisms and adaptive algorithms, two robust control architectures are investigated for surge motion and yaw motion. To guarantee the prespecified performance requirements for position tracking control, the constrained error dynamics are transformed to unconstrained ones by virtue of a tangent-type nonlinear mapping function. On the other hand, the inaccurate model can be identified through radial basis neural networks (RBFNNs), where the minimum learning parameter (MLP) algorithm is employed with a low computational complexity. Furthermore, quantization errors can be effectively reduced even when the parameters of the quantizer remain unavailable to designers. Finally, the effectiveness of the proposed controllers is verified via theoretical analyses and numerical simulations.

Nonlinear Position Control with Augmented Observer in Brushless DC Motor

In this paper, position control using both a nonlinear position controller and a current controller with an augmented observer is proposed for a Brushless DC motor. The nonlinear position controller is designed to improve the position tracking performance based on the tracking error dynamics. The current controller is developed to track the desired currents generated from the desired torque, which is calculated based on the nonlinear position controller. The augmented observer is designed to obtain the knowledge of both state variables and disturbance. Closed-loop stability is proven through the Lyapunov theorem. Simulations were performed to evaluate the effectiveness of the proposed method.

A fast, single-iteration ensemble Kalman smoother for sequential data assimilation

Ensemble-variational methods form the basis of the state-of-the-art for nonlinear, scalable data assimilation, yet current designs may not be cost-effective for reducing prediction error in online, short-range forecast systems. We propose a novel, outer-loop optimization of the ensemble-variational formalism for applications in which forecast error dynamics are weakly nonlinear, such as synoptic meteorology. In order to rigorously derive our method and demonstrate its novelty, we review ensemble smoothers that appear throughout the literature in a unified Bayesian maximum-a-posteriori narrative, updating and simplifying some results. After mathematically deriving our technique, we systematically develop and inter-compare all studied schemes in the open-source Julia package DataAssimilationBenchmarks.jl, with pseudo-code provided for these methods. This high-performance numerical framework, supporting our mathematical results, produces extensive benchmarks that demonstrate the significant performance advantages of our proposed technique. In particular, our single-iteration ensemble Kalman smoother is shown both to improve prediction / posterior accuracy and to simultaneously reduce the leading order cost of iterative, sequential smoothers in a variety of relevant test cases for operational short-range forecasts. This long work is thus intended to present our novel single-iteration ensemble Kalman smoother, and to provide a theoretical and computational framework for the study of sequential, ensemble-variational Kalman filters and smoothers generally.