Maximum Hands-Off Control: A Paradigm of Control Effort Minimization

In this paper, we propose a new paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear

Sparse Packetized Predictive Control for Networked Control over Erasure Channels

We study feedback control over erasure channels with packet-dropouts. To achieve robustness with respect to packet-dropouts, the controller transmits data packets containing plant input predictions, which minimize a finite horizon cost function. To reduce the data size of packets, we propose to adopt sparsity-promoting optimizations, namely, ell-1-ell-2 and ell-2-constrained ell-0 optimizations, for which efficient algorithms exist. We derive sufficient conditions on design parameters, which guarantee (practical) stability of the resulting feedback control systems when the number of consecutive packet-dropouts is bounded.Comment: IEEE Transactions on Automatic Control, Volume 59 (2014), Issue 7 (July) (to appear

FLUTTER SUPPRESSION BY ACTIVE CONTROLLER OF A TWO-DIMENSIONAL WING WITH A FLAP

Flutter is a divergent oscillation of an aeroelastic structure, and one of a family of aeroelastic instability phenomena, that results from the interaction of elastic and inertial forces of the structure with the surrounding aerodynamic forces. Airfoil Flutter is important due to its catastrophic effect on the durability and operational safety of the structure. Traditionally, flutter is prevented within an aircraft\u27s flight envelope using passive approaches such as optimizing stiffness distribution, mass balancing, or modifying geometry during the design phase. Although these methods are effective but they led to heavier airfoil designs. On the other hand, active control methods allow for less weight and higher manoeuvring capabilities. The main objective of this study is to investigate the potential effectiveness of using Model Predictive Control MPC as an active control strategy to suppress flutter. Lagrange’s energy method and Theodore’s unsteady aerodynamic theory were employed to derive the equations of motion of a typical 2D wing section with a flap. Using MATLAB®, the airspeed at which the flutter occurs for a specific wing’s parameters were found to be 23.96 m/s, at a frequency of 6.12 Hz. A Linear Quadratic Gaussian compensator LQG was designed and simulated. MATLAB® was also used to design and simulate a discrete MPC using Laguerre orthonormal functions. The simulated results for states regulation and reference tracking tasks in the flutter airspeed region from both controllers were compared and discussed in terms of quantitative performance measures and performance indices. The results showed that both LQG and MPC are powerful in suppressing the flutter in addition to their effectiveness in tracking a reference input rapidly and accurately with zero steady-state error. The superiority for the constrained MPC is manifested by results comparison. MPC were able to save more than 40% of the needed settling time for states regulation task. Furthermore, it performed the job with much less control energy indicated by the ISE and ISU indices. On top of that, the key advantage of MPC, which is the ability to perform real-time optimization with hard constraints on input variables, was confirmed

Subspace estimation and prediction methods for hidden Markov models

Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite set as well. In particular, we study the geometric structure arising from the nonminimality of the linear state space representation of HMMs, and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix. For this algorithm, we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation, and that the $m$-step linear predictor computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear $m$-step predictor.Comment: Published in at http://dx.doi.org/10.1214/09-AOS711 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust passivity-based control of switched-reluctance motors

International audienceWe propose a state-feedback controller for switched-reluctance motors as a preliminary step towards the solution of the sensorless control problem (without measurement of rotor variables). We establish global exponential stability. Furthermore, our controller renders the closed-loop system robust to external disturbances that is, input-to-state stable. Although there exist some works on sensorless control of switched-reluctance motors, these consist mainly on ad hoc solutions without theoretical foundation. The few theoretically-validated results in the literature are established under more stringent conditions such as knowledge of the load torque

Target Contrastive Pessimistic Discriminant Analysis

Domain-adaptive classifiers learn from a source domain and aim to generalize to a target domain. If the classifier's assumptions on the relationship between domains (e.g. covariate shift) are valid, then it will usually outperform a non-adaptive source classifier. Unfortunately, it can perform substantially worse when its assumptions are invalid. Validating these assumptions requires labeled target samples, which are usually not available. We argue that, in order to make domain-adaptive classifiers more practical, it is necessary to focus on robust methods; robust in the sense that the model still achieves a particular level of performance without making strong assumptions on the relationship between domains. With this objective in mind, we formulate a conservative parameter estimator that only deviates from the source classifier when a lower or equal risk is guaranteed for all possible labellings of the given target samples. We derive the corresponding estimator for a discriminant analysis model, and show that its risk is actually strictly smaller than that of the source classifier. Experiments indicate that our classifier outperforms state-of-the-art classifiers for geographically biased samples.Comment: 9 pages, no figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1706.0808

Data-driven control via Petersen’s lemma

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen’s lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen’s lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through alternate (convex) sum-of-squares programs. The findings are illustrated numerically