Input-to-State Stabilization in H1H^1-Norm for Boundary Controlled Linear Hyperbolic PDEs with Application to Quantized Control

International audienceWe consider a system of linear hyperbolic PDEs where the state at one of the boundary points is controlled using the measurements of another boundary point. For this system class, the problem of designing dynamic controllers for input-to-state stabilization in $H^1$-norm with respect to measurement errors is considered. The analysis is based on constructing a Lyapunov function for the closed-loop system which leads to controller synthesis and the conditions on system dynamics required for stability. As an application of this stability notion, the problem of quantized control for hyperbolic PDEs is considered where the measurements sent to the controller are communicated using a quantizer of finite length. The presence of quantizer yields practical stability only, and the ultimate bounds on the norm of the state trajectory are also derived

Autonomous Behaviors With A Legged Robot

Over the last ten years, technological advancements in sensory, motor, and computational capabilities have made it a real possibility for a legged robotic platform to traverse a diverse set of terrains and execute a variety of tasks on its own, with little to no outside intervention. However, there are still several technical challenges to be addressed in order to reach complete autonomy, where such a platform operates as an independent entity that communicates and cooperates with other intelligent systems, including humans. A central limitation for reaching this ultimate goal is modeling the world in which the robot is operating, the tasks it needs to execute, the sensors it is equipped with, and its level of mobility, all in a unified setting. This thesis presents a simple approach resulting in control strategies that are backed by a suite of formal correctness guarantees. We showcase the virtues of this approach via implementation of two behaviors on a legged mobile platform, autonomous natural terrain ascent and indoor multi-flight stairwell ascent, where we report on an extensive set of experiments demonstrating their empirical success. Lastly, we explore how to deal with violations to these models, specifically the robot\u27s environment, where we present two possible extensions with potential performance improvements under such conditions

Distributed control of deregulated electrical power networks

A prerequisite for reliable operation of electrical power networks is that supply and demand are balanced at all time, as efficient ways for storing large amounts of electrical energy are scarce. Balancing is challenging, however, due to the power system's dimensions and complexity, the low controllability and predictability of demand, and due to strict physical and security limitations, such as finitely fast generator dynamics and finite transmission-line capacities. The need for efficient and secure balancing arrangements is growing stronger with the increasing integration of distributed generation (DG), the ongoing deregulation of production and consumption of electrical energy, and thus, also the provision of many of the ancillary services that are essential for network stability. DG is mostly based on renewable, intermittent sources such as wind and sun, and consequently, it is associated with a much larger uncertainty in supply than conventional, centralized generation. Moreover, with the emergence of deregulated energy markets as core operational mechanism, the prime goal of power system operation is shifted from centralized minimization of costs to the maximization of individual profit by a large number of competing, autonomous market agents. The main objective of this thesis is to investigate the control-technical possibilities for ensuring efficient, reliable and stable operation of deregulated and badly predictable electrical power networks. Its contributions cover aspects of power system operation on a time scale ranging from day-ahead trading of electrical energy to second-based load-frequency control. As a first contribution, we identify the maximization of security of supply and market efficiency as the two main, yet conflicting objectives of power system operation. Special attention is paid to congestion management, which is an aspect of power system operation where the tension between reliability and efficiency is particularly apparent. More specifically, the differences between locational pricing and cost-based congestion redispatch are analyzed, followed by an assessment of their effects on grid operation. Next, we demonstrate that the current synchronous, energy-based market and incentive system does not necessarily motivate producers to exchange power profiles with the electricity grid that contribute to network stability and security of supply. The thesis provides an alternative production scheduling concept as a means to overcome this issue, which relies on standard market arrangements, but settles energy transactions in an asynchronous way. Theoretical analysis and simulation results illustrate that by adopting this method, scheduling efficiency is improved and the strain on balancing reserves can be reduced considerably. A major part of this thesis is dedicated to real-time, i.e., closed-loop, balancing or load-frequency control. With the increasing share of badly predictable DG, there is a growing need for efficient balancing mechanisms that can account for generator and transmission constraints during the operational day. A promising candidate solution is model predictive control (MPC). Because the large dimensions and complexity of electrical power networks hamper a standard, centralized implementation of MPC, we evaluate a number of scalable alternatives, in which the overall control action is computed by a set of local predictive control laws, instead. The extent of inter-controller communication is shown to be positively correlated with prediction accuracy and, thus, attainable closed-loop performance. Iterative, system-wide communication/coordination is usually not feasible for large networks, however, and consequently, Pareto-optimal performance and coupled-constraint handling are currently out of reach. This also hampers the application of standard cost-based stabilization schemes, in which closed-loop stability is attained via monotonic convergence of a single, optimal system-wide performance cost. Motivated by the observations regarding non-centralized MPC, the focus is then shifted to distributed control methods for networks of interconnected dynamical systems, with power systems as particular field of application, that can ensure stability based on local model and state information only. First, we propose a non-centralized, constraint-based stabilization scheme, in which the set of stabilizing control actions is specified via separable convergence conditions for a collection of a-priori synthesized structured max-control Lyapunov functions (max-CLFs). The method is shown to be non-conservative, in the sense that non-monotonic convergence of the structured functions along closed-loop trajectories is allowed, whereas their construction establishes the existence of a control Lyapunov function, and thus, stability, for the full, interconnected dynamics. Then, an alternative method is provided in which also the demand for a monotonically converging full-system CLF is relaxed while retaining the stability certificate. The conditions are embedded in an almost-decentralized Lyapunov-based MPC scheme, in which the local control laws rely on neighbor-to-neighbor communication only. Secondly, a generalized theorem and example system are provided to show that stabilization methods that rely on the off-line synthesis of fixed quadratic storage functions (SFs) fail for even the simplest of linear, time-invariant networks, if they contain one or more subsystems that are not stable under decoupled operation. This may also impede the application of max-CLF control. As key contribution of this thesis, to solve this issue, we endow the storage functions with a finite set of state-dependent parameters. Max-type convergence conditions are employed to construct a Lyapunov function for the full network, whereas monotonic convergence of the individual SFs is not required. The merit of the provided approach is that the storage functions can be constructed during operation, i.e., along a closed-loop trajectory, thus removing the impediment of centralized, off-line LF synthesis associated with fixed-parameter SFs. It is shown that parameterized-SF synthesis conditions can be efficiently exploited to obtain a scalable, trajectory-dependent control scheme that relies on non-iterative neighbor-to-neighbor communication only. For input-affine network dynamics and quadratic storage functions, the procedure can be implemented by solving a single semi-definite program per node and sampling instant, in a receding horizon fashion. Moreover, by interpolating a collection of so-obtained input trajectories, a low-complexity explicit control law for linear, time-invariant systems is obtained that extends the trajectory-specific convergence property to a much stronger guarantee of closed-loop asymptotic stability for a particular set of initial conditions. Finally, we consider the application of max-CLF and parameterized SFs for real-time balancing in multimachine electrical power networks. Given that generators are operated by competitive, profit-driven market agents, the stabilization scheme is extended with the competitive optimization of a set of arbitrarily chosen, local performance cost functions over a finite, receding prediction horizon. The suitability of the distributed Lyapunov-based predictive control and parameterized storage function algorithms is evaluated by simulating them in closed-loop with the 7-machine CIGRÉ benchmark system. The thesis concludes by summarizing the main contributions, followed by ideas for future research

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