Learning-based model predictive control for constrained nonlinear systems

Esta tesis está dedicada al control de sistemas, bajo la hipótesis de que no se conoce nada sobre la dinámica del sistema a controlar. En vez de eso, solamente las entradas y salidas son accesibles, y por tanto se puede tener acceso a un histórico de datos. El objetivo principal es el control de la planta en condiciones eficientes y seguras usando únicamente dichas medidas. Con este fin, se usará un conjunto de métodos de aprendizaje automático conocido como link inferencia, para modelar sistemas no lineales desconocidos, usando controladores predictivos basados en modelo. Por ello, esta tesis presenta contribuciones en dos campos distintos. En primer lugar, se extenderán las técnicas de link inferencia, proponiendo métodos con dos objetivos: reducir tanto el tiempo de cálculo de los algoritmos como el error de predicción cometido por ellos. En segundo lugar, se desarrollarán controladores predictivos robustos y con la habilidad de aprender basándose en datos. Estos controladores serán estables por diseño, capaces de satisfacer restricciones robustamente y de mejorar su actuación beneficiándose de nuevas medidas recogidas en línea

Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Neural Network Based Adaptive Control for Nonlinear Dynamic Regimes

Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named composite model reference adaptive control is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of pseudo-control hedging techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.Ph.D.Committee Chair: Nader Sadegh; Committee Co-Chair: Anthony J. Calise; Committee Member: J.V.R. Prasad; Committee Member: Kok-Meng Lee; Committee Member: Wayne J. Boo

Bounded Influence Approaches to Constrained Mixed Vector Autoregressive Models

The proliferation of many clinical studies obtaining multiple biophysical signals from several individuals repeatedly in time is increasingly recognized, a recognition generating growth in statistical models that analyze cross-sectional time series data. In general, these statistical models try to answer two questions: (i) intra-individual dynamics of the response and its relation to some covariates; and, (ii) how this dynamics can be aggregated consistently in a group. In response to the first question, we propose a covariate-adjusted constrained Vector Autoregressive model, a technique similar to the STARMAX model (Stoffer, JASA 81, 762-772), to describe serial dependence of observations. In this way, the number of parameters to be estimated is kept minimal while offering flexibility for the model to explore higher order dependence. In response to (ii), we use mixed effects analysis that accommodates modelling of heterogeneity among cross-sections arising from covariate effects that vary from one cross-section to another. Although estimation of the model can proceed using standard maximum likelihood techniques, we believed it is advantageous to use bounded influence procedures in the modelling (such as choosing constraints) and parameter estimation so that the effects of outliers can be controlled. In particular, we use M-estimation with a redescending bounding function because its influence function is always bounded. Furthermore, assuming consistency, this influence function is useful to obtain the limiting distribution of the estimates. However, this distribution may not necessarily yield accurate inference in the presence of contamination as the actual asymptotic distribution might have wider tails. This led us to investigate bootstrap approximation techniques. A sampling scheme based on IID innovations is modified to accommodate the cross-sectional structure of the data. Then the M-estimation is applied to each bootstrap sample naively to obtain the asymptotic distribution of the estimates.We apply these strategies to the extracted BOLD activation from several regions of the brain from a group of individuals to describe joint dynamic behavior between these locations. We used simulated data with both innovation and additive outliers to test whether the estimation procedure is accurate despite contamination

Control of Cooperative Haptics-Enabled Teleoperation Systems with Application to Minimally Invasive Surgery

Robot-Assisted Minimally Invasive Surgical (RAMIS) systems frequently have a structure of cooperative teleoperator systems where multiple master-slave pairs are used to collaboratively execute a task. Although multiple studies indicate that haptic feedback improves the realism of tool-tissue interaction to the surgeon and leads to better performance for surgical procedures, current telesurgical systems typically do not provide force feedback, mainly because of the inherent stability issues. The research presented in this thesis is directed towards the development of control algorithms for force reflecting cooperative surgical teleoperator systems with improved stability and transparency characteristics. In the case of cooperative force reflecting teleoperation over networks, conventional passivity based approaches may have limited applicability due to potentially non-passive slave-slave interactions and irregular communication delays imposed by the network. In this thesis, an alternative small gain framework for the design of cooperative network-based force reflecting teleoperator systems is developed. Using the small gain framework, control algorithms for cooperative force-reflecting teleoperator systems are designed that guarantee stability in the presence of multiple network-induced communication constraints. Furthermore, the design conservatism typically associated with the small-gain approach is eliminated by using the Projection-Based Force Reflection (PBFR) algorithms. Stability results are established for networked cooperative teleoperator systems under different types of force reflection algorithms in the presence of irregular communication delays. The proposed control approach is consequently implemented on a dual-arm (two masters/two slaves) robotic MIS testbed. The testbed consists of two Haptic Wand devices as masters and two PA10-7C robots as the slave manipulators equipped with da Vinci laparoscopic surgical instruments. The performance of the proposed control approach is evaluated in three different cooperative surgical tasks, which are knot tightening, pegboard transfer, and object manipulation. The experimental results obtained indicate that the PBFR algorithms demonstrate statistically significant performance improvement in comparison with the conventional direct force reflection algorithms. One possible shortcoming of using PBFR algorithms is that implementation of these algorithms may lead to attenuation of the high-frequency component of the contact force which is important, in particular, for haptic perception of stiff surfaces. In this thesis, a solution to this problem is proposed which is based on the idea of separating the different frequency bands in the force reflection signal and consequently applying the projection-based principle to the low-frequency component, while reflecting the high-frequency component directly. The experimental results demonstrate that substantial improvement in transient fidelity of the force feedback is achieved using the proposed method without negative effects on the stability of the system

Algorithms and Theory for Robust PCA and Phase Retrieval

In this dissertation, we investigate two problems, both of which require the recovery of unknowns from measurements that are potentially corrupted by outliers. The first part focuses on the problem of \emph{robust principal component analysis} (PCA), which aims to recover an unknown low-rank matrix from a corrupted and partially-observed matrix. The robust PCA problem, originally nonconvex itself, has been solved via a convex relaxation based approach \emph{principal component pursuit} (PCP) in the literature. However, previous works assume that the sparse errors uniformly spread over the entire matrix and characterize the condition under which PCP guarantees exact recovery. We generalize these results by allowing non-uniform error corruptions over the low-rank matrix and characterize the conditions on the error corruption probability of each individual entry based on the local coherence of the low-rank matrix, under which correct recovery can be guaranteed by PCP. Our results yield new insights on the graph clustering problem beyond the relevant literature. The second part of the thesis studies the phase retrieval problem, which requires recovering an unknown vector from only its magnitude measurements. Differently from the first part, we solve this problem directly via optimizing nonconvex objectives. As the nonconvex objective is often constructed in such a way that the true vector is its global optimizer, the difficulty here is to design algorithms to find the global optimizer efficiently and provably. In order to solve this problem, we propose a gradient-like algorithm named reshaped Wirtinger flow (RWF). For random Gaussian measurements, we show that RWF enjoys linear convergence to a global optimizer as long as the number of measurements is on the order of the dimension of the unknown vector. This achieves the best possible sample complexity as well as the state-of-the-art computational efficiency. Moreover, we study the phase retrieval problem when the measurements are corrupted by adversarial outliers, which models situations with missing data or sensor failures. In order to resist possible observation outliers in an oblivious manner, we propose a novel median truncation approach to modify the nonconvex approach in both the initialization and the gradient descent steps. We apply the median truncation approach to the Poisson loss and the reshaped quadratic loss respectively, and obtain two algorithms \emph{median-TWF} and \emph{median-RWF}. We show that both algorithms recover the signal from a near-optimal number of independent Gaussian measurements, even when a constant fraction of measurements is corrupted. We further show that both algorithms are stable when measurements are corrupted by both sparse arbitrary outliers and dense bounded noises. We establish our results on the performance guarantee via the development of non-trivial concentration measures of the median-related quantities, which can be of independent interest

Analytic and Learned Footstep Control for Robust Bipedal Walking

Bipedal walking is a complex, balance-critical whole-body motion with inherently unstable inverted pendulum-like dynamics. Strong disturbances must be quickly responded to by altering the walking motion and placing the next step in the right place at the right time. Unfortunately, the high number of degrees of freedom of the humanoid body makes the fast computation of well-placed steps a particularly challenging task. Sensor noise, imprecise actuation, and latency in the sensomotoric feedback loop impose further challenges when controlling real hardware. This dissertation addresses these challenges and describes a method of generating a robust walking motion for bipedal robots. Fast modification of footstep placement and timing allows agile control of the walking velocity and the absorption of strong disturbances. In a divide and conquer manner, the concepts of motion and balance are solved separately from each other, and consolidated in a way that a low-dimensional balance controller controls the timing and the footstep locations of a high-dimensional motion generator. Central pattern generated oscillatory motion signals are used for the synthesis of an open-loop stable walk on flat ground, which lacks the ability to respond to disturbances due to the absence of feedback. The Central Pattern Generator exhibits a low-dimensional parameter set to influence the timing and the landing coordinates of the swing foot. For balance control, a simple inverted pendulum-based physical model is used to represent the principal dynamics of walking. The model is robust to disturbances in a way that it returns to an ideal trajectory from a wide range of initial conditions by employing a combination of Zero Moment Point control, step timing, and foot placement strategies. The simulation of the model and its controller output are computed efficiently in closed form, supporting high-frequency balance control at the cost of an insignificant computational load. Additionally, the sagittal step size produced by the controller can be trained online during walking with a novel, gradient descent-based machine learning method. While the analytic controller forms the core of reliable walking, the trained sagittal step size complements the analytic controller in order to improve the overall walking performance. The balanced whole-body walking motion arises by using the footstep coordinates and the step timing predicted by the low-dimensional model as control input for the Central Pattern Generator. Real robot experiments are presented as evidence for disturbance-resistant, omnidirectional gait control, with arguably the strongest push-recovery capabilities to date

Modeling cerebrocerebellar control in horizontal planar arm movements of humans and the monkey

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (leaves 215-236).In daily life, animals including humans make a wide repertoire of limb movements effortlessly without consciously thinking about joint trajectories or muscle contractions. These movements are the outcome of a series of processes and computations carried out by multiple subsystems within the central nervous system. In particular, the cerebrocerebellar system is central to motor control and has been modeled by many investigators. The bulk of cerebrocerebellar control involves both forward command and sensory feedback information inextricably combined. However, it is not yet clear how these types of signals are reflected in spiking activity in cerebellar cells in vivo. Segmentation of apparently continuous movements was first observed more than a century ago. Since then, submovements, which have been identified by non-smooth speed profiles, have been described in many types of movements. However, physiological origins of submovement have not been well understood. This thesis demonstrates that a currently proposed recurrent integrator PID (RIPID) cerebellar limb control model (Massaquoi 2006a) is consistent with average neural activity recorded in a monkey by developing the Recurrent Integrator-based Cerebellar Simple Spike (RICSS) model.(cont.) The RICSS formulation is consistent with known or plausible cerebrocerebellar and spinocerebellar neurocircuitry, including hypothetical classification of mossy fiber signals. The RICSS model accounts well for variety of cerebellar simple spike activity recorded from the monkey and outperforms any other existing models. The RIPID model is extended to include a simplified cortico-basal ganglionic loop to capture statistical characterization of intermittency observed in individual trials of the monkey. In order to extend the capability of the RIPID model to a larger workspace and faster movements, the model needs to be gainscheduled based on the local state information. A linear parameter varying (LPV) formulation, which shares a similar structure to that suggested by the RICSS model, is performed and its applicability was tested on human subjects performing double step tasks which requires rapid change in movement directions.by Kazutaka Takahashi.Ph.D