On self-learning mechanism for the output regulation of second-order affine nonlinear systems

This paper studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler-Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self learning mechanism, we develop an internal model-based controller that does not require apriori knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control

Stability and Control of Biomolecular Circuits through Structure

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building feedback control through such structures. In this work, we develop the tool of log derivatives to capture structures in how the production and degradation rates of molecules depend on concentrations of reactants. We show that log derivatives could establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through the structures captured. Due to the method's simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations

Mal de Debarquement Syndrome: A Matter of Loops?

Introduction: Mal de Debarquement Syndrome (MdDS) is a poorly understood neurological disorder affecting mostly perimenopausal women. MdDS has been hypothesized to be a maladaptation of the vestibulo-ocular reflex, a neuroplasticity disorder, and a consequence of neurochemical imbalances and hormonal changes. Our hypothesis considers elements from these theories, but presents a novel approach based on the analysis of functional loops, according to Systems and Control Theory. Hypothesis: MdDS is characterized by a persistent sensation of self-motion, usually occurring after sea travels. We assume the existence of a neuronal mechanism acting as an oscillator, i.e., an adaptive internal model, that may be able to cancel a sinusoidal disturbance of posture experienced aboard, due to wave motion. Thereafter, we identify this mechanism as a multi-loop neural network that spans between vestibular nuclei and the flocculonodular lobe of the cerebellum. We demonstrate that this loop system has a tendency to oscillate, which increases with increasing strength of neuronal connections. Therefore, we hypothesize that synaptic plasticity, specifically long-term potentiation, may play a role in making these oscillations poorly damped. Finally, we assume that the neuromodulator Calcitonin Gene-Related Peptide, which is modulated in perimenopausal women, exacerbates this process thus rendering the transition irreversible and consequently leading to MdDS. Conclusion and Validation: The concept of an oscillator that becomes noxiously permanent can be used as a model for MdDS, given a high correlation between patients with MdDS and sea travels involving undulating passive motion, and an alleviation of symptoms when patients are re-exposed to similar passive motion. The mechanism could be further investigated utilizing posturography tests to evaluate if subjective perception of motion matches with objective postural instability. Neurochemical imbalances that would render individuals more susceptible to developing MdDS could be investigated through hormonal profile screening. Alterations in the connections between vestibular nuclei and cerebellum, notably GABAergic fibers, could be explored by neuroimaging techniques as well as transcranial magnetic stimulation. If our hypothesis were tested and verified, optimal targets for MdDS treatment could be found within both the neural networks and biochemical factors that are deemed to play a fundamental role in loop functioning and synaptic plasticity

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)

Adaptive Output Regulation For Multivariable Nonlinear Systems Via Hybrid Identification Techniques

Output regulation refers to the class of control problems in which some outputs of the controlled system must be steered to some desired references, while maintaining closed-loop stability and in spite of the presence of unmeasured disturbances and model uncertainties. While for linear systems the problem has been elegantly solved in the 70s, output regulation for nonlinear systems is still a challenging research field, and 30 years of active research left open many fundamental problems. In particular, all the regulators proposed so far are limited to very specific classes of nonlinear systems and, even in those cases, they fail in extending in their full generality the celebrated properties of the linear regulator. The aim of this thesis is to make a decisive step towards the systematic extension of the output regulation theory to embrace more general multivariable problems. To this end, we touch here three fundamental pillars of regulation theory: the structure of regulators, the robustness issue, and the adaptation of the control system. Regarding the structural aspects, we pursue here a design paradigm that is complementary to canonical nonlinear regulators and that trades a conceptually more suitable structure with a strong internal intertwining between the different parts of the regulator. For what concerns robustness, we introduce a new framework to characterize robustness of regulators relative to steady-state properties more general than the usual requirement asking a zero asymptotic error. We characterize in this unifying terms a large part of the existing approaches, and we end conjecturing that general nonlinear regulation admits no robust solution. Regarding the evolution of regulators, we propose an adaptive regulation framework in which adaptation is used online to tune the internal models embedded in the control system. Adaptation is cast as a general system identification problem, allowing for different well-known algorithms to be used

Internal Models in Control, Biology and Neuroscience

This tutorial paper deals with the Internal Model Principle (IMP) from different perspectives. The goal is to start from the principle as introduced and commonly used in the control theory and then enlarge the vision to other fields where 'internal models' play a role. The biology and neuroscience fields are specifically targeted in the paper. The paper ends by presenting an 'abstract' theory of IMP applicable to a large class of systems