A normal vector approach for integrated process and control design with uncertain model parameters and disturbances

This paper presents a new approach for robust open-loop and closed-loop control of nonlinear processes with parameter uncertainties and a comparison with classical concepts. The approach leads to trajectories that show small variations if uncertain parameters and uncertain initial conditions are present. The algorithm utilizes the Unscented Transformation. It allows a 2nd order approximation of the first two statistical moments of the system's output as a function of the stochastic system's state and uncertain model parameters. Because the numerical burden is low, it can be used for optimization based online closed-loop process control as well.

A new approach for robust model predictive control of biological production processes

A novel active disturbance rejection control (ADRC) solution and a particular tuning method are presented for a class of time delay system (TDS) with uncertainty. First, the complicated process dynamics is modeled as a simple first order plus large time delay (FOPTD) plant, with the difference between the actual dynamics and its model treated as disturbances to be rejected. Then the reduced order linear extended state observer (RLESO) with input delay is proposed to estimate the time delay state and disturbance. It is shown how the time delay could be eliminated from the characteristic equation of the closed-loop system by manipulations of controller parameters. Secondly, the one parameter tuning (OPT) technique is developed where all controller parameters are made function of a single coefficient. In comparison with optimal proportional-integral-derivative (PID) controller and twice optimum controller (TOC), the simulation results show that the proposed method not only has better accuracy and faster response, but also ensures better robustness and adaptability against uncertain model parameters and external disturbances, especially for the plant with very large time delays.

The linear Kalman-Bucy filter with both uncertain second-order statistical noise properties and uncertain system model parameters is considered. We investigate the conditions for robust stability based on the upper norm-bound of noise and parametrical uncertainties. Saddlepoint theory and the Gronwall lemma are employed to solve this problem.

The trajectory tracking method for an unmanned surface vehicle (USV) using integral terminal sliding mode integral backstepping adaptive control (ITSMIBAC) scheme is presented in this paper, which takes into account external disturbances and uncertain model parameters. Furthermore, finite-time convergence and excellent track tracking effect are guaranteed by the differential equations that is made up of the integral terminal sliding mode function. In particular, a backstepping method adding integral term is used to ensure the globally asymptotic stability of system and make the differential equations to converge to zero. The upper bound of the disturbances including external disturbances and uncertain model parameters is estimated by an adaptive control law. Finally, the effectiveness and the feasibility of the proposed controller are demonstrated by numerical example and comparison result through tracking circular orbit.

This paper presents an approach for robust open-loop and closed-loop control of nonlinear processes with safety constraints. The approach leads to trajectories that establish a dynamic safety margin if uncertain parameters and uncertain initial conditions are present. The algorithm utilizes the Unscented Transformation. It allows a 2nd order approximation of the first two statistical moments of the system's output as a function of the stochastic system's state and uncertain model parameters. Because the numerical burden is low, it can be used for optimization based online closed-loop process control as well.

Design of a stable adaptive nonlinear observer for an exothermic stirred tank reactor

A self-tuning PID (Proportion-Integral-Derivative) control method based on the adaptive mechanism was proposed for the magnetic suspension active vibration isolation system with the characteristics of nonlinear, time-varying, and model parameter uncertainty. The controller identified the controlled object parameters online and solved the controller parameters in real time. To test the effectiveness of the proposed method, a six degree-of-freedom (DOF) magnetic suspension active vibration isolation system was designed and built. The six DOF dynamic model of the vibration isolation system with uncertain model parameters was derived for control. Experiments were carried out and compared with the control effects of the tradition PID control and cascade PID control algorithm. The experimental results show that the proposed self-tuning PID controller has more outstanding practicality and effectiveness in solving the model parameter uncertainty problem compared with the existing studies at home and abroad, and it also proves that the control method has a good isolation effect on the wide band disturbances.

This article continues a recent line of research that uses so-called solution invariants to enhance the accuracy of fast interval methods for bounding the reachable sets of nonlinear ODEs under uncertainty. The term solution invariants refers to algebraic state constraints that are implied by the dynamics. These can either exist naturally in the model (i.e., conservation laws) or they can be deliberately introduced by ‘lifting’ to achieve tighter bounds. While such reachability methods have proven very effective in some cases, they are limited in the types of invariants that can be used. In this article, we first present an important theoretical extension that permits the use of invariants that depend on uncertain model parameters. Next, we develop an extension of existing algorithms that enables the use of general nonlinear invariants for the first time. These extensions are demonstrated on an uncertain dynamic model of an anaerobic digestion process.

This paper investigates a trajectory tracking control method for multi-underactuated underwater vehicle (AUV) formations with uncertain model parameters and external environmental disturbances. Firstly, a dual closed-loop fixed-time integral sliding mode controller is designed. By combining fixed-time theory and integral sliding mode control, this controller ensures the stability of the formation tracking and guarantees the convergence of the tracking error to zero within a fixed time duration. Secondly, an adaptive radial basis function (RBF) neural network controller is integrated with a conditional integrator to address uncertainties in model parameters, approximation errors, and external environmental disturbances in practical multi-AUV systems. This controller exhibits robustness and adaptivity. Additionally, a virtual leader strategy is employed to enhance the robustness of the formation system and prevent formation collapse caused by leader AUV failures. Finally, simulation results validate the effectiveness of the proposed formation controller, demonstrating accurate trajectory tracking by the AUV formation.

This investigation focuses on design-under-uncertainty problems that employ a probabilistic performance as objective function and consider its estimation through stochastic simulation. This approach puts no constraints on the computational and probability models adopted, but involves a high computational cost especially for design problems involving complex, high-fidelity numerical models. A framework relying on kriging metamodeling to approximate the system performance in an augmented input space is considered here to alleviate this cost. A sub region of the design space is defined and a kriging metamodel is built to approximate the system response (output) with respect to both the design variables and the uncertain model parameters (random variables). This metamodel is then used within a stochastic simulation setting (addressing uncertainties in the model parameters) to approximate the system performance when estimating the objective function for specific values of the design variables. This information is then used to search for a local optimum within the previously established design sub domain. Only when the optimization algorithm drives the search outside this domain, a new metamodel is generated. The process is iterated until convergence is established and an efficient sharing of information across these iterations is established to adaptively tune characteristics of the kriging metamodel.

With respect to the accurate tracking control for unmanned surface vehicles (USVs), this paper proposes a novel hierarchical control structure consisting of a velocity planner and a tracking controller. With full consideration of control accuracy and tracking safety, a model predictive control planning method based on dynamic artificial potential field method (DAPF-MPC) is proposed, aiming to generate the current optimal reference tracking velocity and achieve online obstacle avoidance guidance. Simultaneously, a fixed-time generalized super-twisting controller based on an extended state observer (ESO-FiTGST) is proposed to restrict the convergence time and tackle with challenge resulting from the uncertain disturbances and model parameters. Noticeably, the design process of the proposed control law and its rigorous stability analysis, especially for the computable fixed-time convergence property, are detailed. Ultimately, the simulation and experimental results demonstrate the superiority and feasibility of the proposed method, providing a reliable and effective reference solution for tracking control tasks of USVs in aquatic scenarios with complex obstacles.

In this paper, the problems of robust consensus tracking control for the second-order multi-agent system with uncertain model parameters and nonlinear disturbances are considered. An adaptive control strategy is proposed to smooth the agent’s trajectory, and the neural network is constructed to estimate the system’s unknown components. The consensus conditions are demonstrated for tracking a leader with nonlinear dynamics under an adaptive control algorithm in the absence of model uncertainties. Then, the results are extended to the system with unknown time-varying disturbances by applying the neural network estimation to compensating for the uncertain parts of the agents’ models. Update laws are designed based on the Lyapunov function terms to ensure the effectiveness of robust control. Finally, the theoretical results are verified by numerical simulations, and a comparative experiment is conducted, showing that the trajectories generated by the proposed method exhibit less oscillation and converge faster.

High-dimensional uncertainty quantification for Mars atmospheric entry using adaptive generalized polynomial chaos

Climate models are subject to high parametric uncertainty induced by poorly confined model parameters of parameterized physical processes. Uncertain model parameters are typically calibrated in order to increase the agreement of the model with available observations. The common practice is to adjust uncertain model parameters manually, often referred to as expert tuning, which lacks objectivity and transparency in the use of observations. These shortcomings often haze model inter‐comparisons and hinder the implementation of new model parameterizations. Methods which would allow to systematically calibrate model parameters are unfortunately often not applicable to state‐of‐the‐art climate models, due to computational constraints facing the high dimensionality and non‐linearity of the problem. Here we present an approach to objectively calibrate a regional climate model, using reanalysis driven simulations and building upon a quadratic metamodel presented by Neelin et al. (2010) that serves as a computationally cheap surrogate of the model. Five model parameters originating from different parameterizations are selected for the optimization according to their influence on the model performance. The metamodel accurately estimates spatial averages of 2 m temperature, precipitation and total cloud cover, with an uncertainty of similar magnitude as the internal variability of the regional climate model. The non‐linearities of the parameter perturbations are well captured, such that only a limited number of 20–50 simulations are needed to estimate optimal parameter settings. Parameter interactions are small, which allows to further reduce the number of simulations. In comparison to an ensemble of the same model which has undergone expert tuning, the calibration yields similar optimal model configurations, but leading to an additional reduction of the model error. The performance range captured is much wider than sampled with the expert‐tuned ensemble and the presented methodology is effective and objective. It is argued that objective calibration is an attractive tool and could become standard procedure after introducing new model implementations, or after a spatial transfer of a regional climate model. Objective calibration of parameterizations with regional models could also serve as a strategy toward improving parameterization packages of global climate models.