Full-State Feedback of Uncertain Multi-Input Systems

2020 ◽  
pp. 134-168
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Adaptive Control ◽  
Delay Systems ◽  
Global Stabilization ◽  
State Estimator ◽  
The Third ◽  
State Measurement ◽  
Full State ◽  
Full State Feedback ◽  
Single Input

This chapter investigates adaptive control for uncertain multi-input LTI systems with distinct discrete actuator delays. In parallel with the single-input case in the third chapter, four types of basic uncertainties come with multi-input LTI time-delay systems. Different combinations of the four uncertainties above result in different design difficulties. For example, when the full-state measurement of the transport PDE state is available, the global stabilization is acquired, whereas when the actuator state is not measurable and the delay value is unknown at the same time, the problem is not solvable globally, since the problem is not linearly parameterized. The chapter then summarizes the different collections of uncertainties for the multi-input case. When some of the four variables are unknown or unmeasured, the basic idea of certainty-equivalence-based adaptive control is to use an estimator (a parameter estimator or a state estimator) to replace the unknown variables in the PDE-based framework in the previous chapter, and carefully select their adaptive update laws based on Lyapunov-based analysis.

Simple adaptive control to attenuate bridge’s seismic responses considering parametric variations

2019 ◽  
Vol 23 (1) ◽  
pp. 132-145
Author(s):  
Rachel W Soares ◽  
Luciana R Barroso ◽  
Omar AS Al-Fahdawi
Keyword(s):  
Adaptive Control ◽  
Performance Criteria ◽  
Seismic Responses ◽  
Control Approach ◽  
Control Schemes ◽  
Full State ◽  
Full State Feedback ◽  
Bridge Structures ◽  
Parametric Change ◽  
Adaptive Control Algorithm

Parametric variations occur throughout a bridge’s service life as a result of temperature variations, cracking, localized damage, and fatigue. Existing bridge’s parameters are difficult to estimate precisely and implemented control schemes may perform unsatisfactorily depending on how sensitive they are to parametric change. In this study, an adaptive control approach is developed utilizing the simple adaptive control algorithm and designed aiming to mitigate seismic responses of bridges considering realistic implementation. Adaptive control is a viable alternative to control bridge structures as it is able to calculate control gains that vary over time based on sensed responses, sustaining performance in face of parametric variations. The proposed approach allows the choice of a model reference of significantly low order and it does not require full-state feedback or the use of observers. The effectiveness and robustness of the control approach are investigated when controlling a seismically excited two-span highway bridge considering systematic parametric variations. Evaluation of relevant performance criteria indicates that the adaptive scheme is effective in reducing seismic responses and sustains well the overall performance when systematic parametric variations are introduced. The proposed approach requires a small and reasonable number of sensors to present effectiveness and performs satisfactorily even when in the presence of measurement noise.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

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