Robust adaptive control of nonlinear non-minimum phase systems with uncertainties

This paper, presents a robust adaptive control method for a class of nonlinear non-minimum phase systems with uncertainties. The development of the control method comprises two steps. First, stabilization of the system is considered based on the availability of the output and internal dynamics of the system. The reference signal is designed to stabilize the internal dynamics with respect to the output tracking error. Moreover, a combined neuro-adaptive controller is proposed to guarantee asymptotic stability of the tracking error. Then, the overall stability is achieved using the small gain theorem. Next, the availability of internal dynamics is relaxed by using a linear error observer. The unmatched uncertainty is compensated using a suitable reference signal. The ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the Lyapunov theory. The theoretical results are applied to a translational oscillator/rotational actuator model to illustrate the effectiveness of the proposed scheme.     

Nonlinear model-state feedback control for nonminimum-phase processes

A general nonlinear controller design methodology for continuous-time nonminimum-phase systems is presented, which utilizes synthetic outputs that are statically equivalent to the original process outputs and make the system minimum-phase. A systematic procedure is proposed for the construction of statically equivalent outputs with prescribed transmission zeros. The calculated outputs are used to construct a model-state feedback controller. The proposed method is applied to a nonminimum-phase chemical reactor control problem where a series/parallel reaction is taking place.     

Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.     

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

In the above paper Makoudi and Radouane, 2000 [A robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay. Automatica, 36, 1057-1065.], a model reference adaptive control (MRAC) algorithm is presented for non-minimum phase systems with unknown or time-varying delays. Unfortunately, this paper contains several mathematical mistakes that render the proofs of the claimed results erroneous. Furthermore, there are no obvious ways to correct these errors, so that the results presented in this paper are questionable.     

On the effect of additional input channels on the achievable performance of discrete-time control systems

This paper deals with the quantification of performance bounds in multiple-input multiple-output (MIMO) control systems when energy-constrained input channels are added to the plant. We focus on stable, discrete-time, linear time-invariant (LTI), and right-invertible MIMO systems. The performance is quantified using the 2-norm and assuming step references, whilst the control input energy constraint is on the increments of the additional input signals. Our main result is a closed form expression that quantifies the improvement in performance that results as a consequence of the additional input channels.     

Nonlinear iterative learning control with applications to lithographic machinery

An experimental demonstration is given of (nonlinear) iterative learning control applied to a reticle stage of a lithographic wafer scanner. To limit the presence of noise in the learned forces, a nonlinear amplitude-dependent learning gain is proposed. With this gain, high-amplitude signal contents is separated from low-amplitude noise, the former being compensated by the learning algorithm. Contrary to the underlying linear design, the continuously varying trade-off between high-gain convergence rates and low-gain noise transmission demonstrates a significant improvement of the nonlinear design in achieving performance.     

Using stable input-output inversion for minimum-time feedforward constrained regulation of scalar systems

The paper approaches the feedforward minimum-time smooth control of non-minimum-phase linear scalar systems for set-point regulation. The aim is to synthesize a bounded input subject to non-saturating constraints on the input and its derivatives till a prespecified arbitrary order. The provided solution relies on a stable input-output dynamic inversion technique and an ad hoc parameterized family of output transition functions. The synthesized minimum-time input that exhibits pre- and post-actuation is determined by means of easily-implementable closed-form expressions. Examples are given to illustrate the methodology.     

Optimal feedforward compensators for systems with right-half plane zeros

Feedforward from measurable disturbances is a powerful complement to feedback control to improve disturbance rejection capability. Recent works have remarked the necessity of a design strategy for those cases where the ideal feedforward controller is not realizable. In this paper, a simple shaping design procedure is presented together with straightforward rules to obtain optimal feedforward controllers for the case when the ideal compensator is not realizable due to right-half plane zeros in the process dynamics. Finally, some simulations and a robustness analysis demonstrate the benefits of the proposed tuning rules.     

基于状态相关系数系统的非线性控制

针对非线性仿射系统的镇定问题,将待镇定系统表达成相应的状态相关系数系统.在短时段内,可以用一个线性定常系统逼近该状态相关系数系统,将该线性定常系统的镇定控制器用来控制原非线性系统.该设计方法的优点是:设计简单,只用到线性定常系统的控制方法,无需构造复杂的李亚普诺夫函数;扩展容易,可以结合各种线性系统设计方法进行控制器设计.在状态相关系数矩阵满足可换性条件时,可以保证闭环系统的稳定性.对小车倒立摆的仿真结果表明:用该设计方法构造的控制器可以很好地镇定系统.     

Nonlinear optimal tracking control with application to super-tankers for autopilot design

A new method is introduced to design optimal tracking controllers for a general class of nonlinear systems. A recently developed recursive approximation theory is applied to solve the nonlinear optimal tracking control problem explicitly by classical means. This reduces the nonlinear problem to a sequence of linear-quadratic and time-varying approximating problems which, under very mild conditions, globally converge in the limit to the nonlinear systems considered. The converged control input from the approximating sequence is then applied to the nonlinear system. The method is used to design an autopilot for the ESSO 190,000-dwt oil tanker. This multi-input-multi-output nonlinear super-tanker model is well established in the literature and represents a challenging problem for control design, where the design requirement is to follow a commanded maneuver at a desired speed. The performance index is selected so as to minimize: (a) the tracking error for a desired course heading, and (b) the rudder deflection angle to ensure that actuators operate within their operating limits. This will present a trade-off between accurate tracking and reduced actuator usage (fuel consumption) as they are both mutually dependent on each other. Simulations of the nonlinear super-tanker control model are conducted to illustrate the effectiveness of the nonlinear tracking controller.     

Nonlinear modelling and control of helicopters

This paper presents the development of a nonlinear model and of a nonlinear control strategy for a VARIO scale model helicopter. Our global interest is a 7-DOF (degree-of-freedom) general model to be used for the autonomous forward-flight of helicopter drones. However, in this paper we focus on the particular case of a reduced-order model (3-DOF) representing the scale model helicopter mounted on an experimental platform. Both cases represent underactuated systems ( for the 7-DOF model and for the 3-DOF model studied in this paper). The proposed nonlinear model possesses quite specific features which make its study an interesting challenge, even in the 3-DOF case. In particular aerodynamical forces result in input signals and matrices which significantly differ from what is usually considered in the literature on mechanical systems control. Numerical results and experiments on a scale model helicopter illustrate the theoretical developments, and robustness with respect to parameter uncertainties is studied.     

Generalized bang-bang control for feedforward constrained regulation

In the behavioral framework for continuous-time linear scalar systems, simple sufficient conditions for the solution of the minimum-time rest-to-rest feedforward constrained control problem are provided. The investigation of the time-optimal input-output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure. The resulting optimal input is composed of sequences of bang-bang functions and linear combinations of the modes associated to the zero dynamics. This signal behavior constitutes a generalized bang-bang control that can be fruitfully exploited for feedforward constrained regulation. Using discretization, an arbitrarily good approximation of the optimal generalized bang-bang control is found by solving a sequence of linear programming problems. Numerical examples are included.     

线性时滞系统前馈-反馈次优控制: Taylor 级数法

研究线性时滞系统最优控制的前馈反馈近似设计问题.基于Taylor级数法,将系统的二次型最优控制问题转化为线性代数方程组的求解问题,给出了系统前馈反馈次优控制律的存在唯一性条件和Taylor级数表示形式.仿真算例验证了方法的有效性.     

Global stabilization of feedforward systems with exponentially unstable Jacobian linearization

The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high-gain feedback saturated at a low level. The control law forces the derivatives of the state variables to small values along the closed-loop trajectories. This “slow control” design is illustrated with a benchmark example and its limitations are emphasized.     

An acceleration measurements-based approach for helicopter nonlinear flight control using Incremental Nonlinear Dynamic Inversion

Due to the inherent instabilities and nonlinearities of rotorcraft dynamics, its changing properties during flight and the engineering difficulties to predict its aerodynamics with high levels of fidelity, helicopter flight control requires the application of special strategies. These strategies must allow to cope with the nonlinearities of the system and assure robustness in the presence of inaccuracies and changes in configuration.In this paper, a novel approach based on an Incremental Nonlinear Dynamic Inversion is applied to simplify the design of helicopter flight controllers. With this strategy, by employing the feedback of acceleration measurements to avoid the need for information relative to any aerodynamic change, the control system does not need any model data that depends exclusively on its states, thus enhancing its robustness to model uncertainties.The overall control system is tested by simulating two tasks with distinct agility levels as described in the ADS-33 helicopter handling qualities standard. The analysis shows that the controller provides an efficient tracking of the commanded references. Furthermore, with the robustness properties verified within the range of inaccuracies expected to be found in reality, this novel method seems to be eligible for a potential practical implementation to helicopter vehicles.     

一类非最小相位非线性系统的直接自适应控制

一类非最小相位非线性系统的直接自适应控制韩存武,袁少强,马晓军,文传源（北京航空航天大学自控系北京１０００８３）关键词：非线性系统,自适应控制,非最小相位系统．１引言非线性系统的自适应控制作为当前自动控制领域最富有挑战性、同时也最困难的前沿课题之一越...     

Nonlinear model predictive control with polytopic invariant sets

Ellipsoidal invariant sets have been widely used as target sets in model predictive control (MPC). These sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope. The choice of inclusion polytope has a significant effect on the size of the target ellipsoid, but the optimal inclusion polytope cannot in general be computed systematically. This paper shows that use of polytopic invariant sets overcomes this difficulty, allowing larger stabilizable sets without loss of performance. In the interests of online efficiency, consideration is focused on interpolation-based MPC.     

一类非最小相位非线性系统的自适应控制

针对一类非最小相位的非线性系统,通过引入一个近似系统,提出了一种简单的间接自适应控制方法,并分析了采用该方法后系统输出的跟踪性能,给出了输出跟踪误差的上限.该方法可克服现有的非线性自适应控制方法只能控制最小相位的非线性系统并且容易产生过度控制的缺点.     

Suboptimal control for nonlinear systems: a successive approximation approach

This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear systems with a quadratic performance index. By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation examples are employed to test the validity of the SAA.     

Risk-sensitive control for a class of nonlinear systems with multiplicative noise

In this paper, we consider the problem of optimal control for a class of nonlinear stochastic systems with multiplicative noise. The nonlinearity consists of quadratic terms in the state and control variables. The optimality criteria are of a risk-sensitive and generalised risk-sensitive type. The optimal control is found in an explicit closed-form by the completion of squares and the change of measure methods. As applications, we outline two special cases of our results. We show that a subset of the class of models which we consider leads to a generalised quadratic–affine term structure model (QATSM) for interest rates. We also demonstrate how our results lead to generalisation of exponential utility as a criterion in optimal investment.