We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials SONC. Additionally, it provides a candidate for the global minimizer. By branching over the signs of the variables, we improve the bounds even further, with only a moderate increase in the running time.
As a result, a classic approach consists in "squaring down" the plant, by combining some of the control inputs in order to obtain a model having as many inputs as outputs, to which standard theory can be applied and unique solutions arise. In this talk, a different perspective is taken, showing that the presence of more inputs than outputs ushers in the possibility of achieving better performance or extra features by exploiting the extra degrees of freedom through optimization.
Examples will be given by showing performance improvement at non-trivial not just constant steady-state solutions, the interest for nonlinear solutions in otherwise linear output regulation problems, and the use of input reconfiguration to unveil otherwise stealthy attacks in cyber-physical systems.
In particular the properties of the propulsion system and their variability during the operational life of the spacecraft have a degree of uncertainty that can affect the overall system design and the reliability of the design solution. This talk will present an approach to model this epistemic uncertainty with Dempster-Shafer theory of Evidence and to compute robust and reliable guidance laws that optimise a performance index and satisfy a number of constraints.
The approach is applied to the case of a low-thrust transfer from the Earth to an asteroid. The talk will present also a method to compute optimal guidance laws in the case uncertainty is propagated with a generalised polynomial algebra based on Chebyshev expansions. Gonzalez Abstract: Many control problems - coming from very different areas that go from diseases treatments, to spacecraft guidance, passing through electronic and Nanoelectronic control- fell into the framework of what is called impulsive control: "a control paradigm based on impulsive differential equations in which a nonimpulsive plant has at least one impulsively changeable state variable".
More precisely, we are interested in nonimpulsive plants linear, time variant or invariant, continuous-time systems controlled by impulsive actions, i. Such systems have some particularities: they have no formal equilibriums out of the origin, they can be characterized by two discrete time sub-models describing the system just before and after the discontinuity the jumps , their stability has to be defined in terms of two generalized equilibria, etc.
Among the control strategies able to account for the impulsive schemes, model predictive control MPC is one of the most promising ones, because of its well-known benefits constraint satisfaction, optimality, stability, etc. More important, MPC is able to account for the stability of equilibrium or invariant sets, instead of points, which means that once the closed-loop system reaches any point or trajectory in the target set, no further control actions are implemented i.
In this talk, the details of a particular impulsive zone MPC formulation will be discussed. As a first step, a linear impulsive system characterization is made, which includes two discrete-time sub-systems and extended equilibrium and invariant sets, even in regions far from the origin. Then, an MPC formulation that takes advantage of the aforementioned characterization is presented.
The main idea is to exploit the proper uses of artificial optimization variables and output target zones, which allows us to have an enlarged domain of attraction and preserves the stability and recursive feasibility of the closed loop. To motivate the potential application of the strategy, some simulation examples are proposed. They satisfy various properties for analyzing nonconvex and nonsmooth optimization problems. For instance, they satisfy a theorem akin to the uniform limit theorem in analysis regarding continuous functions. Global functions are also endowed with properties regarding the composition of functions and change of variables.
Using these results, we show that a class of nonconvex and nonsmooth optimization problems arising in tensor decomposition applications are global functions. This provides a theoretical guarantee for the l1 norm to avoid outliers in nonconvex optimization. Also, game theory is a quantitative method to understand conflicts and contentions among players or systems.
These features make the theory an appropriate tool to model and design secure and resilient cyber-physical and human systems. In this talk, we will first give a short introduction to the theory and its applications. Then, we will present a meta-game approach to the multi-layer and multi-type cyber and physical interactions to provide a holistic analytical framework for assessing cyber risks of CPS under advanced persistent threats. We will leverage the theory as a guideline for developing security-hardening strategies for the network security and designing resilient controllers to respond to failures.
We use the Internet of Controlled Things and the autonomous systems as case stu! Although the general class of such dynamics is difficult to deal with in numerical analysis and synthesis, some subclasses are relatively easy. The dynamics determined by a Markov chain is a solid example of such subclasses and has been extensively studied in the field of Markov jump systems. In this study, on the other hand, we focus on as another subclass the stochastic dynamics determined by a process that is i.
We discuss equivalence of some stability notions for the systems with such dynamics, and show a Lyapunov inequality condition that is necessary and sufficient for their stability. Since our Lyapunov inequality will involve decision variables contained in the expectation operation, an idea is provided to solve it as a standard LMI linear matrix inequality. The idea can be further exploited in stabilization state feedback synthesis for the systems.
This important feature is motivated by the use of observers in output feedback control and it has been proved that this tunability property plays a key role in establishing a nonlinear separation principle. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks.
Mainly: numerical issues due to the fact that we need to implement coefficients which increases polynomially with the system dimension; the well-known peaking phenomenon; high sensitivity to measurement noise. The low-power high-gain observers are characterized by having coefficients which does not grow with the system dimension, by avoiding the peaking phenomenon and by improving the sensitivity to high-frequency measurement noise. The proposed observers can be used without loss of generality with respect to standard high-gain observers in frameworks of observations, output feedback or output regulation.
The first technique is for generation of points on the stable manifold in a robust way against numerical errors.
There, a special numerical method that preserves Hamiltonian is used to solve a differential equation sensitive to numerical errors. The second technique is a sort of shooting method to generate a point corresponding to the desired system state. These techniques are used for optimal swing-up of a pendulum and successfully give a swing-up trajectory with multiple swings. This is a joint work with Noboru Sakamoto and Takuto Nakamura.
However, this cannot happen without addressing proper attention to the soundness of these algorithms. This work discusses the formal verification of convex optimization algorithms with a particular emphasis on receding-horizon controllers. Additionally, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the code level, thereby making it accessible for the formal methods community.
In seeking zero-bug software, we use the Credible Autocoding scheme. We focused our attention on the ellipsoid algorithm solving second-order cone programs SOCP. In addition to this, we present a floating-point analysis of the algorithm and give a framework to numerically validate the method. Such networked control systems NCS are much harder to design and analyse because the communication network introduces a range of undesirable effects into the closed loop system, such as the sampling jitter, quantized signals, the need for signal scheduling, data dropouts, and so on.
In this talk I will concentrate on control oriented modelling of NCS with WirelessHART networks and then present results on an emulation oriented approach for achieving Lp stabilisation of such systems. We show that our results are less conservative in an appropriate sense than prior emulation results that do not exploit the specific network structure in the analysis. The background and idea of glocal control are explained by showing the control perspective of IoT Internet of Things.
The key for realization of glocal control is hierarchical networked dynamical systems with multiple resolutions in time and space depending on the layer. After introducing a unified framework, its fundamental control theory such as stability and robust stability is provided. Through the talk we show the effectiveness of the theoretical results for applications to electric vehicle control and power network systems towards smart cities.
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