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Register a new userTracking Control by the Newton-Raphson Method with Output Prediction and Controller Speedup
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This paper presents a control technique for output tracking of reference signals in continuous-time dynamical systems. The technique is comprised of the following three elements: (i) output prediction which has to track the reference signal, (ii) a controller based on an integrator with variable gain, and (iii) a speedup of the control action for enhancing the trackers accuracy and, in some cases, guaranteeing stability of the closed-loop system. The technique is suitable for linear and nonlinear systems, implementable by simple algorithms, can track reference points as well as time-dependent reference signals, and may have large, even global domains of attraction. The derived theoretical results include convergence of the tracking controller and error analysis, and are supported by illustrative simulation and laboratory experiments.
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This paper concerns applications of a recently-developed output-tracking technique to trajectory control of autonomous vehicles. The technique is based on three principles: Newton-Raphson flow for solving algebraic equations,output prediction, and controller speedup. Early applications of the technique, made to simple systems of an academic nature,were implemented by simple algorithms requiring modest computational efforts. In contrast, this paper tests it on commonly-used dynamic models to see if it can handle more complex control scenarios. Results are derived from simulations as well as a laboratory setting, and they indicate effective tracking convergence despite the simplicity of the control algorithm.
An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a generalized equation. To its numerical solution we apply the semismooth* Newton method by Gfrerer and Outrata (2019) in which, in contrast to most available Newton-type methods for inclusions, one approximates not only the single-valued but also the multi-valued part. This is performed on the basis of limiting (Morduchovich) coderivative. In our case of the Tresca friction, the multi-valued part amounts to the subdifferential of a convex function generated by the friction and contact conditions. The full 3D discrete problem is then reduced to the contact boundary. Implementation details of the semismooth* Newton method are provided and numerical tests demonstrate its superlinear convergence and mesh independence.
This paper deals with suboptimal distributed H2 control by dynamic output feedback for homogeneous linear multi-agent systems. Given a linear multi-agent system, together with an associated H2 cost functional, the objective is to design dynamic output feedback protocols that guarantee the associated cost to be smaller than an a priori given upper bound while synchronizing the controlled network. A design method is provided to compute such protocols. The computation of the two local gains in these protocols involves two Riccati inequalities, each of dimension equal to the dimension of the state space of the agents. The largest and smallest nonzero eigenvalue of the Laplacian matrix of the network graph are also used in the computation of one of the two local gains.A simulation example is provided to illustrate the performance of the proposed protocols.
Recently developed control methods with strong disturbance rejection capabilities provide a useful option for control design. The key lies in a general concept of disturbance and effective ways to estimate and compensate the disturbance. This work extends the concept of disturbance as the mismatch between a system model and the true dynamics, and estimates and compensates the disturbance for multi-input multi-output linear/nonlinear systems described in a general form. The results presented do not need to assume the disturbance to be independent of the control inputs or satisfy a certain matching condition, and do not require the system to be expressible in an integral canonical form as required by algorithms previously described in literature. The estimator and controller are designed under a state tracking framework, and sufficient conditions for the closed-loop stability are presented. The performance of the resulting controller relies on a co-design of the system model, the state and disturbance observer, and the controller. Numerical experiments on a first-order system and an inverted pendulum under uncertainties are used to illustrate the control design method and demonstrate its efficacy.
In PDE-constrained optimization, proper orthogonal decomposition (POD) provides a surrogate model of a (potentially expensive) PDE discretization, on which optimization iterations are executed. Because POD models usually provide good approximation quality only locally, they have to be updated during optimization. Updating the POD model is usually expensive, however, and therefore often impossible in a model-predictive control (MPC) context. Thus, reduced models of mediocre quality might be accepted. We take the view of a simplified Newton method for solving semilinear evolution equations to derive an algorithm that can serve as an offline phase to produce a POD model. Approaches that build the POD model with impulse response snapshots can be regarded as the first Newton step in this context. In particular, POD models that are based on impulse response snapshots are extended by adding a second simplified Newton step. This procedure improves the approximation quality of the POD model significantly by introducing a moderate amount of extra computational costs during optimization or the MPC loop. We illustrate our findings with an example satisfying our assumptions.
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