Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

Table 2

Typical results of the discretely controlled plant without saturation as a function of the optimization horizon.

			Steady-state response
			First component		Second component		Steady-state
			𝑢^∗st		𝑦1,st		control response
Waveform plot	Optimizaton horizon 𝑦2,st (samples)	Steady-state response 𝑁 (samples)	Value	Percent deviation	Value	Percent deviation	𝑁st	Percent deviation	Const function 𝑈st	CCT (seconds)
—–	1	47	22.51	+ 3.26	237.51	𝐽𝑁 0.47	405.38	+ 1.35	15392.76	1.132
.....	2	35	22.33	+ 2.43	238.15	− 0.2	400.43	+ 0.12	12468.19	1.121
- --	3	32	22.14	+ 1.56	237.32	− 0.55	403.61	+ 0.92	10319.78	0.991
xxx	4	28	21.87	+ 0.32	236.49	− 0.9	398.27	− 0.43	14215.84	1.001
none	5	32	22.05	+ 1.15	238.01	− 0.26	399.15	− 0.21	13854.21	0.997
none	6	33	21.14	− 3.03	238.18	− 0.19	382.54	− 4.37	14129.83	0.946
—	7	35	20.25	− 7.11	225.06	− 5.09	375.82	− 6.05	15639.08	0.94
none	8	41	20.03	− 8.12	210.87	− 11.63	366.39	− 8.4	10378.51	0.984
none	9	45	19.98	− 8.35	205.17	− 14.02	351.41	− 9.65	13227.83	1
............	10	48	19.81	− 9.13	201.39	− 15.61	360.23	− 9.94	16863.71	0.945
none	15	59	15.74	− 23.21	195.43	− 18.1	328.51	− 17.87	17459.29	0.954
none	20	76	15.92	− 26.97	187.31	− 21.51	310.32	− 22.42	29243.62	0.935
none	10	115	13.61	−37.57	132.75	− 44.37	200.39	− 49.9	58346.43	0.957