Minimum energy controllers with inequality constraints on output variances. (English) Zbl 0688.93068
Summary: We consider the design of control systems to minimize the input energy subject to output variance inequality constraints. Necessary and sufficient conditions are developed for state feedback, measurement feedback and dynamic controllers. We find that all these problems are equivalent to LQ problems with a diagonal output weighting matrix \({\mathbb{Q}}\), where \({\mathbb{Q}}\) has some interesting properties which reflect the importance of each constraint.
An algorithm which iteratively selects the weight \({\mathbb{Q}}\) is given. Similar results are also derived for the dual problem where input variance inequality constraints are desired. All these results can be applied to the deterministic case with inequality constraints on the \(L_{\infty}\)-norm of the outputs.
An algorithm which iteratively selects the weight \({\mathbb{Q}}\) is given. Similar results are also derived for the dual problem where input variance inequality constraints are desired. All these results can be applied to the deterministic case with inequality constraints on the \(L_{\infty}\)-norm of the outputs.
MSC:
| 93E20 | Optimal stochastic control |
| 49K45 | Optimality conditions for problems involving randomness |
| 93C05 | Linear systems in control theory |
References:
| [1] | Skelton, J. Guidance 8 pp 454– (1985) |
| [2] | Moden, IEEE Trans. Automatic Control AC-27 pp 214– (1982) |
| [3] | Toivonen, Automatica 19 pp 415– (1983) |
| [4] | and , Linear Optimal Control Systems, Wiley, New York, 1972. |
| [5] | Makila, Automatica 20 pp 15– (1984) |
| [6] | Toivonen, Int. J. Control 37 pp 493– (1983) · Zbl 0509.93043 |
| [7] | Makila, Optim. control, appl. methods 3 pp 337– (1982) |
| [8] | Toivonen, Int. J. Control 38 pp 229– (1983) · Zbl 0509.93043 |
| [9] | and , ’Design of linear regulators with energy constraints’, Proc. IEEE CDC, 1980, pp. 301–305; |
| [10] | also in Control, Identification, and Input Optimization, Plenum Press, New York, 1985, pp. 96–105 |
| [11] | The Calculus of Variations and Optimal Control, Plenum Press, New York, 1981. · doi:10.1007/978-1-4899-0333-4 |
| [12] | Zadeh, IEEE Trans. Automatic Control AC-8 pp 59– (1963) |
| [13] | Lin, IEEE Trans. Automatic Control AC-21 pp 641– (1976) |
| [14] | ’Covariance control for dynamic systems’, AIAA Guidance & Control Conf., Minneapolis, August, 1988. |
| [15] | , and , Purdue Internal Report, 1986. |
| [16] | and , Purdue Internal Report, 1988. |
| [17] | , , , and , Purdue Internal Report, 1989. |
| [18] | Linear and Nonlinear Programming, Addison-Wesley, Reading, MA, 1984. |
| [19] | Axsäter, Int. J. Control 4 pp 549– (1966) |
| [20] | Levine, IEEE Trans. Automatic Control AC-15 pp 44– (1970) |
| [21] | Johnson, IEEE Trans. Automatic Control AC-15 pp 658– (1970) |
| [22] | Levine, IEEE Trans. Automatic Control AC-16 pp 785– (1971) |
| [23] | McLane, Int. J. Control 13 pp 383– (1971) · Zbl 0224.93055 |
| [24] | Horisberger, IEEE Trans. Automatic Control AC-19 pp 434– (1974) |
| [25] | Kurtaran, Int. J. Control 19 pp 497– (1974) |
| [26] | Choi, IEEE Trans. Automatic Control AC-19 pp 257– (1974) |
| [27] | Sidar, Int. J. Control 22 pp 377– (1975) |
| [28] | Basuthakur, IEEE Trans. Automatic. Control AC-20 pp 664– (1975) |
| [29] | Wenk, IEEE Trans. Automatic Control AC-25 pp 496– (1980) |
| [30] | Hyland, IEEE Trans. Automatic Control AC-29 pp 1034– (1984) |
| [31] | Toivonen, Int. J. Control 46 pp 897– (1987) · Zbl 0652.93032 |
| [32] | ’A homotopy algorithm for solving the optimal projection equations for fixed-order dynamic compensation: existence, convergence and global optimality’, Proc. ACC, June 1987, pp. 1527–1531. |
| [33] | ’Convolution and Hankel operator norms for linear systems’, IEEE CDC, pp. 1373–1374, Austin, December 1988. |
| [34] | , and , ’Robustness properties of covariance controllers’, Allerton Conf., Monticello, Illinois, September 1989. |
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