This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified.
more »
« less
Chance Constraint based design of Input Shapers
The focus of this paper is on the design of input
shapers for systems with uncertainties in the parameters of the
vibratory modes which need to be attenuated. A probabilistic
framework is proposed for the design of the robust input
shaper, when the uncertain modal parameters are characterized
by probability density functions. A convex chance constrained
optimization problem is posed to determine the parameters of
input shapers (time-delay filter) which can accommodate the
users acceptable risk levels for a prescribed residual energy
threshold. Robust input shapers are developed for various
compact support distributions to illustrate the ability of the
proposed formulation to synthesize input shapers which can
satisfy a residual energy threshold with a given risk level. This
problem formulation can conceivably reduce the conservative
nature of worst case controllers which have to ensure that all
realizations of the uncertain system have to satisfy a prescribed
performance index. The chance constrained input shaper is
designed for a spring-mass-dashpot system with three different
distributions for the uncertain spring stiffness. Results provide
encouragement for the extension of the proposed approach to
multi-dimensional and multi-model uncertainties.
more »
« less
- Award ID(s):
- 1537210
- NSF-PAR ID:
- 10113122
- Date Published:
- Journal Name:
- 2017 IEEE Conference on Control Technology and Applications
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. We first review three categories of existing methods to chance-constrained optimization: (1) scenario approach; (2) sample average approximation; and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Key results of the analytical reformulation approach for specific distributions are briefly discussed. We then provide a comprehensive review on the applications of chance-constrained optimization in power systems. Finally, this paper provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases.more » « less
-
For linear dynamic systems with uncertain parameters, design of controllers which drive a system from an initial condition to a desired final state, limited by state constraints during the transition is a nontrivial problem. This paper presents a methodology to design a state constrained controller, which is robust to time invariant uncertain variables. Polynomial chaos (PC) expansion, a spectral expansion, is used to parameterize the uncertain variables permitting the evolution of the uncertain states to be written as a polynomial function of the uncertain variables. The coefficients of the truncated PC expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A transformation of PC polynomial space to the Bernstein polynomial space permits determination of bounds on the evolving states of interest. Linear programming (LP) is then used on the deterministic set of equations with constraints on the bounds of the states to determine the controller. Numerical examples are used to illustrate the benefit of the proposed technique for the design of a rest-to-rest controller subject to deformation constraints and which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass-damper system.more » « less
-
In a chance constrained program (CCP), decision makers seek the best decision whose probability of violating the uncertainty constraints is within the prespecified risk level. As a CCP is often nonconvex and is difficult to solve to optimality, much effort has been devoted to developing convex inner approximations for a CCP, among which the conditional value-at-risk (CVaR) has been known to be the best for more than a decade. This paper studies and generalizes the ALSO-X, originally proposed by Ahmed, Luedtke, SOng, and Xie in 2017 , for solving a CCP. We first show that the ALSO-X resembles a bilevel optimization, where the upper-level problem is to find the best objective function value and enforce the feasibility of a CCP for a given decision from the lower-level problem, and the lower-level problem is to minimize the expectation of constraint violations subject to the upper bound of the objective function value provided by the upper-level problem. This interpretation motivates us to prove that when uncertain constraints are convex in the decision variables, ALSO-X always outperforms the CVaR approximation. We further show (i) sufficient conditions under which ALSO-X can recover an optimal solution to a CCP; (ii) an equivalent bilinear programming formulation of a CCP, inspiring us to enhance ALSO-X with a convergent alternating minimization method (ALSO-X+); and (iii) an extension of ALSO-X and ALSO-X+ to distributionally robust chance constrained programs (DRCCPs) under the ∞−Wasserstein ambiguity set. Our numerical study demonstrates the effectiveness of the proposed methods.more » « less
-
null (Ed.)For energy-efficient Connected and Automated Vehicle (CAV) Eco-driving control on signalized arterials under uncertain traffic conditions, this paper explicitly considers traffic control devices (e.g., road markings, traffic signs, and traffic signals) and road geometry (e.g., road shapes, road boundaries, and road grades) constraints in a data-driven optimization-based Model Predictive Control (MPC) modeling framework. This modeling framework uses real-time vehicle driving and traffic signal data via Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) communications. In the MPC-based control model, this paper mathematically formulates location-based traffic control devices and road geometry constraints using the geographic information from High-Definition (HD) maps. The location-based traffic control devices and road geometry constraints have the potential to improve the safety, energy, efficiency, driving comfort, and robustness of connected and automated driving on real roads by considering interrupted flow facility locations and road geometry in the formulation. We predict a set of uncertain driving states for the preceding vehicles through an online learning-based driving dynamics prediction model. We then solve a constrained finite-horizon optimal control problem with the predicted driving states to obtain a set of Eco-driving references for the controlled vehicle. To obtain the optimal acceleration or deceleration commands for the controlled vehicle with the set of Eco-driving references, we formulate a Distributionally Robust Stochastic Optimization (DRSO) model (i.e., a special case of data-driven optimization models under moment bounds) with Distributionally Robust Chance Constraints (DRCC) with location-based traffic control devices and road geometry constraints. We design experiments to demonstrate the proposed model under different traffic conditions using real-world connected vehicle trajectory data and Signal Phasing and Timing (SPaT) data on a coordinated arterial with six actuated intersections on Fuller Road in Ann Arbor, Michigan from the Safety Pilot Model Deployment (SPMD) project.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
