Output feedback control of nonlinear systems with uncertain ISS/iISS supply rates and noises

This paper considers the problem of global output feedback control for a class of nonlinear systems with inverse dynamics. The main contribution of paper is that: For the inverse dynamics with uncertain ISS/iISS supply rates, and the systems being disturbed by L2 noises, we construct a reduced-order observer-based output feedback controller, which drives the output of system to zero and maintain other closed-loop signals bounded. Finally, a simulation example shows the effectiveness of the control scheme

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

Robust Output Regulation for Autonomous Robots:self-learning mechanisms, task-space control and multi-agent systems

This thesis focuses on robust output regulation for autonomous robots. The control objective of output regulation is to design a feedback controller to achieve asymptotic tracking and/or disturbance rejection for a class of exogenous reference and/or disturbance while maintaining closed-loop stability. We investigate three research problems that pertain to the constructive design of robust output regulation for fully actuated Euler-Lagrange systems from centralized to distributed fashions. The first one is the global robust output regulation of second-order affine nonlinear systems with input disturbances that encompass the fully-actuated Euler-Lagrange systems. Based on a certainty equivalence principle method, we proposed a novel class of nonlinear internal models taking a cascade interconnection structure with strictly relaxed conditions than before. The second one is the output regulation for robot manipulators working in task-space. An internal model-based adaptive controller is designed to cope with uncertain manipulator kinematic and dynamic parameters, as well as unknown periodic reference trajectories generated by harmonic oscillators. The last one is the formation control of manipulators’ end-effector subject to external disturbances or parameter uncertainties. We present and analyze gradient descent-based distributed formation controllers for end-effectors. Internal models are used to reject external disturbances. Moreover, by introducing an extra integrator and an adaptive estimator for gravitational compensation and stabilization, respectively, we extend the proposed gradient-based design to the case where the plant parameters are not exactly known

Adaptive control for time-varying systems: congelation and interconnection

This thesis investigates the adaptive control problem for systems with time-varying parameters. Two concepts are developed and exploited throughout the thesis: the congelation of variables, and the active nodes. The thesis first revisits the classical adaptive schemes and explains the challenges brought by the presence of time-varying parameters. Then, the concept of congelation of variables is introduced and its use in combinations with passivity-based, immersion-and-invariant, and identification-based adaptive schemes are discussed. As the congelation of variables method introduces additional interconnection in the closed-loop system, a framework for small-gain-like control synthesis for interconnected systems is needed.\vspace{2ex} To this end, the thesis proceeds by introducing the notion of active nodes. This is instrumental to show that as long as a class of node systems that possess adjustable damping parameters, that is the active nodes, satisfy certain graph-theoretic conditions, the desired small-gain-like property for the overall system can be enforced via tuning these adjustable parameters. Such conditions for interconnected systems with quadratic, nonlinear, and linearly parametrized supply rates, respectively, are elaborated from the analysis and control synthesis perspectives. The placement and the computation/adaptation of the damping parameters are also discussed. Following the introduction of these two fundamental tools, the thesis proceeds by discussing state-feedback designs for a class of lower-triangular nonlinear systems. The backstepping technique and the congelation of variables method are combined for passivity-based, immersion-and-invariance, and identification-based schemes. The notion of active nodes is exploited to yield simple and systematic proofs. Based on the results established for lower-triangular systems, the thesis continues to investigate output-feedback adaptive control problems. An immersion-and-invariance scheme for single-input single-output linear systems and a passivity-based scheme for nonlinear systems in observer form are proposed. The proof and interpretation of these results are also based on the notion of active nodes. The simulation results show that the adaptive control schemes proposed in the thesis have superior performance when compared with the classical schemes in the presence of time-varying parameters. Finally, the thesis studies two applications of the theoretical results proposed. The servo control problem for serial elastic actuators, and the disease control problem for interconnected settlements. The discussions show that these problems can be solved efficiently using the framework provided by the thesis.Open Acces

Nonsmooth Adaptive Control Design for a Large Class of Uncertain High-Order Stochastic Nonlinear Systems

This paper investigates the problem of the global stabilization via partial-state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns and stochastic zero dynamics. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the problem, a lot of substantial technical difficulties should be overcome since the presence of severe uncertainties/unknowns, unmeasurable zero dynamics, and stochastic noise. By introducing the suitable adaptive updated law for an unknown design parameter and appropriate control Lyapunov function, and by using the method of adding a power integrator, an adaptive continuous (nonsmooth) partial-state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one. A simulation example is provided to illustrate the effectiveness of the proposed approach

Distributed Cooperative Control of Multi-Agent Systems Under Detectability and Communication Constraints

Cooperative control of multi-agent systems has recently gained widespread attention from the scientific communities due to numerous applications in areas such as the formation control in unmanned vehicles, cooperative attitude control of spacecrafts, clustering of micro-satellites, environmental monitoring and exploration by mobile sensor networks, etc. The primary goal of a cooperative control problem for multi-agent systems is to design a decentralized control algorithm for each agent, relying on the local coordination of their actions to exhibit a collective behavior. Common challenges encountered in the study of cooperative control problems are unavailable group-level information, and limited bandwidth of the shared communication. In this dissertation, we investigate one of such cooperative control problems, namely cooperative output regulation, under various local and global level constraints coming from physical and communication limitations. The objective of the cooperative output regulation problem (CORP) for multi-agent systems is to design a distributed control strategy for the agents to synchronize their state with an external system, called the leader, in the presence of disturbance inputs. For the problem at hand, we additionally consider the scenario in which none of the agents can independently access the synchronization signal from their view of the leader, and therefore it is not possible for the agents to achieve the group objective by themselves unless they cooperate among members. To this end, we devise a novel distributed estimation algorithm to collectively gather the leader states under the discussed detectability constraint, and then use this estimation to synthesize a distributed control solution to the problem. Next, we extend our results in CORP to the case with uncertain agent dynamics arising from modeling errors. In addition to the detectability constraint, we also assumed that the local regulated error signals are not available to the agents for feedback, and thus none of the agents have all the required measurements to independently synthesize a control solution. By combining the distributed observer and a control law based on the internal model principle for the agents, we offer a solution to the robust CORP under these added constraints. In practical applications of multi-agent systems, it is difficult to consistently maintain a reliable communication between the agents. By considering such challenge in the communication, we study the CORP for the case when agents are connected through a time-varying communication topology. Due to the presence of the detectability constraint that none of the agents can independently access all the leader states at any switching instant, we devise a distributed estimation algorithm for the agents to collectively reconstruct the leader states. Then by using this estimation, a distributed dynamic control solution is offered to solve the CORP under the added communication constraint. Since the fixed communication network is a special case of this time-varying counterpart, the offered control solution can be viewed as a generalization of the former results. For effective validation of previous theoretical results, we apply the control algorithms to a practical case study problem on synchronizing the position of networked motors under time-varying communication. Based on our experimental results, we also demonstrate the uniqueness of derived control solutions. Another communication constraint affecting the cooperative control performance is the presence of network delays. To this regard, first we study the distributed state estimation problem of an autonomous plant by a network of observers under heterogeneous time-invariant delays and then extend to the time-varying counterpart. With the use of a low gain based estimation technique, we derive a sufficient stability condition in terms of the upper bound of the low gain parameter or the time delay to guarantee the convergence of estimation errors. Additionally, when the plant measurements are subject to bounded disturbances, we find that that the local estimation errors also remain bounded. Lastly, by using this estimation, we present a distributed control solution for a leader-follower synchronization problem of a multi-agent system. Next, we present another case study concerning a synchronization control problem of a group of distributed generators in an islanded microgrid under unknown time-varying latency. Similar to the case of delayed communication in aforementioned works, we offer a low gain based distributed control protocol to synchronize the terminal voltage and inverter operating frequency

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)

On Iterative Learning in Multi-agent Systems Coordination and Control

Ph.DDOCTOR OF PHILOSOPH